Edit Profile (opens in new tab) Mandelbrot, Benoit B. Compute Distance To: Compute Author ID: mandelbrot.benoit-b Published as: Mandelbrot, Benoit B.; Mandelbrot, Benoît B.; Mandelbrot, Benoit; Mandelbrot, Benoît; Mandelbrot, B. B.; Mandelbrot, B. more...less External Links: MacTutor · MGP · Wikidata · dblp · GND · IdRef Documents Indexed: 120 Publications since 1951, including 16 Books 3 Contributions as Editor · 4 Further Contributions Biographic References: 50 Publications Co-Authors: 40 Co-Authors with 40 Joint Publications 1,405 Co-Co-Authors all top 5 Co-Authors 83 single-authored 7 Barral, Julien 5 Frame, Michael Lee 4 Riedi, Rudolf H. 3 Cioczek-Georges, Renata 3 Evertsz, Carl J. G. 2 Coppens, Marc-Olivier 2 Hudson, Richard L. 2 Jaffard, Stéphane 2 Jin, Xiong 2 Jones, Peter Wilcox 2 Kahane, Jean-Pierre 2 Peitgen, Heinz-Otto 2 Stauffer, Dietrich 2 Taqqu, Murad S. 2 Van Ness, John W. 2 Yekutieli, Iddo 1 Abernathy, Robert 1 Aharony, Amnon 1 Atiyah, Michael Francis 1 Barnsley, Michael Fielding 1 Berger, J. M. 1 Borel, Armand 1 Chaitin, Gregory John 1 Chao, Ren 1 Chomsky, Noam Avram 1 Dauben, Joseph Warren 1 Devaney, Robert L. 1 Douady, Adrien 1 Eilenberg, G. 1 Fisher, Yuval 1 Franke, Herbert W. 1 Friedan, Daniel Harry 1 Gleason, H. A. jun. 1 Glimm, James G. 1 Goodman, Nelson 1 Gray, Jeremy John 1 Gutzwiller, Martin C. 1 Hadamard, Jacques 1 Halle, Morris 1 Harary, Frank 1 Herzberger, Hans G. 1 Hirsch, Morris W. 1 Hiz, Henry 1 Hockett, Charles F. 1 Jakobson, Roman 1 Kaufman, Henry 1 Lambek, Joachim 1 Mac Lane, Leslie Saunders 1 McCamy, K. 1 McGuire, Michael 1 Oettinger, Anthony G. 1 Peterson, Gordon E. 1 Peyrière, Jacques 1 Putnam, Hilary Whitehall 1 Quine, Willard Van Orman 1 Richter, Peter H. 1 Rose, I. H. 1 Rubin, Robert J. 1 Ruelle, David Pierre 1 Samorodnitsky, Gennady Pinkhosovich 1 Sapoval, Bernard 1 Saupe, Dietmar 1 Schwarz, Albert S. 1 Shlesinger, Michael F. 1 Steen, Lynn Arthur 1 Thom, René 1 Uhlenbeck, Karen Keskulla 1 Vicsek, Tamás 1 Voss, Richard F. 1 Wallis, James R. 1 Wells, Rulon 1 Witten, Edward 1 Yngve, Victor H. 1 Zeeman, Erik Christopher all top 5 Serials 11 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 5 The Mathematical Intelligencer 5 Journal of Physics A: Mathematical and General 5 Quantitative Finance 5 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 3 Information and Control 3 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 3 Advances in Applied Mathematics 2 Journal of Fluid Mechanics 2 Journal of Statistical Physics 2 Physica A 2 Econometrica 2 International Economic Review 2 The Annals of Applied Probability 2 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 2 Stochastic Processes and their Applications 2 Fractals 2 Physica Scripta 2 Annals of Finance 1 IEEE Transactions on Information Theory 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Advances in Mathematics 1 Gazette des Mathématiciens 1 Journal of Applied Probability 1 Publications de l’Institut de Statistique de l’Université de Paris 1 Physica D 1 Probability Theory and Related Fields 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Review 1 Bulletin of the American Mathematical Society. New Series 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Bernoulli 1 Symmetry: Culture and Science 1 The Journal of Fourier Analysis and Applications 1 International Journal of Fracture 1 Bulletin de l’Institut International de Statistique 1 Bulletin of the International Statistical Institute 1 MAA Notes 1 Proceedings of Symposia in Applied Mathematics 1 Annals of Mathematical Statistics 1 Transactions of the IRE Professional Group on Information Theory all top 5 Fields 59 Measure and integration (28-XX) 40 Probability theory and stochastic processes (60-XX) 26 Dynamical systems and ergodic theory (37-XX) 15 General and overarching topics; collections (00-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 History and biography (01-XX) 11 Fluid mechanics (76-XX) 8 Functions of a complex variable (30-XX) 8 Statistical mechanics, structure of matter (82-XX) 5 General topology (54-XX) 4 Geometry (51-XX) 4 Statistics (62-XX) 3 Real functions (26-XX) 2 Mathematical logic and foundations (03-XX) 2 Number theory (11-XX) 2 Convex and discrete geometry (52-XX) 2 Computer science (68-XX) 2 Information and communication theory, circuits (94-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Relativity and gravitational theory (83-XX) 1 Biology and other natural sciences (92-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 99 Publications have been cited 4,327 times in 3,541 Documents Cited by ▼ Year ▼ The fractal geometry of nature. Rev. ed. of “Fractals”, 1977. Zbl 0504.28001Mandelbrot, Benoit B. 1,162 1982 Fractional Brownian motions, fractional noises and applications. Zbl 0179.47801Mandelbrot, B. B.; Van Ness, J. W. 1,132 1968 Fractals. Form, chance, and dimension. Translation. Zbl 0376.28020Mandelbrot, Benoit B. 247 1977 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. Zbl 0289.76031Mandelbrot, Benoit B. 236 1974 Fractals and scaling in finance. Discontinuity, concentration, risk. Zbl 1005.91001Mandelbrot, Benoit B. 178 1997 The beauty of fractals. Images of complex dynamical systems. Zbl 0601.58003Peitgen, H.-O.; Richter, P. H. 135 1986 On the quadratic mapping \(z\rightarrow z^{2}-\mu \) for complex \(\mu \) and \(z\): the fractal structure of its set, and scaling. Zbl 1194.30028Mandelbrot, Benoit B. 125 1983 Multifractal products of cylindrical pulses. Zbl 1014.60042Barral, Julien; Mandelbrot, Benoît B. 73 2002 The Pareto-Lévy law and the distribution of income. Zbl 0201.51101Mandelbrot, B. 73 1960 Some noises with \(1/f\) spectrum, a bridge between direct current and white noise. Zbl 0148.40507Mandelbrot, Benoit 56 1967 Fractals. Form, chance and dimension. (Les objets fractals. Forme, hasard et dimension.) Zbl 0900.00018Mandelbrot, Benoît B. 51 1975 The fractal geometry of nature. Sonderausgabe. (Die fraktale Geometrie der Natur. Übers. aus dem Englischen von Reinhilt Zähle und Ulrich Zähle.) Zbl 0925.28001Mandelbrot, Benoît B. 51 1991 Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence. Zbl 0227.76081Mandelbrot, Benoit B. 47 1972 Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire. Zbl 0276.60096Mandelbrot, Benoit 41 1974 Multifractals and 1/f noise. Wild self-affinity in physics (1963–1976). Selecta volume. Zbl 0956.28005Mandelbrot, Benoît B. 38 1999 A class of micropulses and antipersistent fractional Brownian motion. Zbl 0846.60055Cioczek-Georges, Renata; Mandelbrot, Benoît B. 36 1995 Limit theorems on the self normalized range for weakly and strongly dependent processes. Zbl 0288.60033Mandelbrot, Benoit B. 36 1975 Gaussian self-affinity and fractals. Globality, the earth, \(1/f\) noise, and R/S. Selecta (old or new) volume H. With contributions by F. J. Damerau, M. Frame, K. McCamy, J. W. Van Ness, J. R. Wallis, and others. Selected works of Benoit B. Mandelbrot. Zbl 1007.01020Mandelbrot, Benoit B. 34 2002 Robust R/S analysis of long-run serial correlation. Zbl 0518.62036Mandelbrot, Benoit B.; Taqqu, Murad S. 34 1979 The (mis)behavior of markets. A fractal view of risk, ruin and reward. Zbl 1140.91004Mandelbrot, Benoit B.; Hudson, Richard L. 33 2004 Self-affine fractals and fractal dimension. Zbl 1063.28500Mandelbrot, Benoit B. 31 1985 Renewal sets and random cutouts. Zbl 0234.60102Mandelbrot, Benoit B. 30 1972 Long-run linearity, locally Gaussian process, H-spectra and infinite variances. Zbl 0191.51002Mandelbrot, B. 27 1969 Alternative micropulses and fractional Brownian motion. Zbl 0879.60076Cioczek-Georges, R.; Mandelbrot, Benoît B. 25 1996 Fractal geometry: What is it, and what does it do! Zbl 0746.00012Mandelbrot, B. B. 24 1989 Fractal aspects of the iteration of \(z \to \lambda z(1-z)\) for complex \(\lambda\) and z. Zbl 0478.58017Mandelbrot, Benoit B. 23 1980 Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire: quelques extensions. Zbl 0276.60097Mandelbrot, Benoit 23 1974 On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars. Zbl 0329.76047Mandelbrot, Benoit B. 23 1975 Negative fractal dimensions and multifractals. Zbl 0713.58034Mandelbrot, Benoit B. 23 1990 The science of fractal images. With contributions by Yuval Fisher and Michael McGuire. Ed. by Heinz-Otto Peitgen and Dietmar Saupe. (Based on notes for the course fractals - introduction, basics and pespectives given as part of the SIG-GRAPH ’87, Anaheim, Calif. course program). Zbl 0683.58003Barnsley, Michael F.; Devaney, Robert L.; Mandelbrot, Benoit B.; Peitgen, Heinz-Otto; Saupe, Dietmar; Voss, Richard 20 1988 Convergence of complex multiplicative cascades. Zbl 1221.60028Barral, Julien; Jin, Xiong; Mandelbrot, Benoît 19 2010 Random multiplicative multifractal measures. II: Non-degeneracy, moments, dimension, and multifractal analysis for random multiplicative measures. Zbl 1117.28007Barral, Julien; Mandelbrot, Benoît B. 17 2004 Local regularity of nonsmooth wavelet expansions and application to the Polya function. Zbl 0916.42024Jaffard, Stéphane; Mandelbrot, Benoît B. 16 1996 Fractals and chaos. The Mandelbrot set and beyond. Selecta volume C. With a foreword by P. W. Jones and texts co-authored by C. J. G. Evertsz and M. C. Gutzwiller. Zbl 1076.01037Mandelbrot, Benoit B. 15 2004 Multifractal formalism for infinite multinomial measures. Zbl 0866.28005Riedi, Rudolf H.; Mandelbrot, Benoît B. 14 1995 The role of sufficiency and of estimation in thermodynamics. Zbl 0111.33705Mandelbrot, B. 14 1962 Abraham Robinson. The creation of nonstandard analysis, a personal and mathematical odyssey. With a foreword by Benoit B. Mandelbrot. Zbl 0933.01025Dauben, Joseph Warren 13 1995 On Dvoretzky coverings for the circle. Zbl 0222.60044Mandelbrot, Benoit B. 13 1972 Random multiplicative multifractal measures. I: Introduction to infinite products of independent random functions. Zbl 1088.28004Barral, Julien; Mandelbrot, Benoît B. 12 2004 Measures of fractal lacunarity: Minkowski content and alternatives. Zbl 0841.28010Mandelbrot, Benoît B. 12 1995 A population birth-and-mutation process. I.: Explicit distributions for the number of mutants in an old culture of bacteria. Zbl 0287.60093Mandelbrot, Benoit 12 1974 Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism. Zbl 0850.76277Mandelbrot, Benoît B. 11 1991 Exceptions to the multifractal formalism for discontinuous measures. Zbl 0892.28008Riedi, Rudolph H.; Mandelbrot, Benoît B. 11 1998 Uniform convergence for complex [0,1]-martingales. Zbl 1208.60035Barral, Julien; Jin, Xiong; Mandelbrot, Benoît 10 2010 Stable paretian random functions and the multiplicative variation of income. Zbl 0104.38402Mandelbrot, Benoit 10 1961 Une classe de processus stochastiques homothetiques à soi; application à la loi climatologique de H.E. Hurst. Zbl 0127.09501Mandelbrot, B. 10 1965 Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3 + B. Zbl 0372.76043Mandelbrot, Benoit 10 1976 The canopy and shortest path in a self-contacting fractal tree. Zbl 1052.28500Mandelbrot, Benoit B.; Frame, Michael 10 1999 Responses to “Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics”, by A. Jaffe and F. Quinn. Zbl 0803.01014Atiyah, Michael; Borel, Armand; Chaitin, G. J.; Friedan, Daniel; Glimm, James; Gray, Jeremy J.; Hirsch, Morris W.; MacLane, Saunders; Mandelbrot, Benoit B.; Ruelle, David; Schwarz, Albert; Uhlenbeck, Karen; Thom, René; Witten, Edward; Zeeman, Christopher 9 1994 Inversion formula for continuous multifractals. Zbl 0892.28007Riedi, Rudolf H.; Mandelbrot, Benoît B. 9 1997 Sur certains prix spéculatifs: faits empiriques et modèle basé sur les processus stables additifs non gaussiens de Paul Lévy. Zbl 0100.34904Mandelbrot, Benoit 9 1962 Multifractal power law distributions: Negative and critical dimensions and other “anomalies”, explained by a simple example. Zbl 1026.28007Mandelbrot, Benoit B. 8 2003 Inverse measures, the inversion formula, and discontinuous multifractals. Zbl 0870.28004Mandelbrot, Benoît B.; Riedi, Rudolf H. 8 1997 Multiperiodic multifractal martingale measures. Zbl 1047.28003Barral, J.; Coppens, M.-O.; Mandelbrot, B. B. 8 2003 A note on a class of skew distribution functions: Analysis and critique of a paper by H. A. Simon. Zbl 0101.11303Mandelbrot, Benoit 8 1959 Fractional multiplicative processes. Zbl 1201.60035Barral, Julien; Mandelbrot, Benoît 8 2009 Stable fractal sums of pulses: The cylindrical case. Zbl 0844.60017Cioczek-Georges, Renata; Mandelbrot, Benoît B.; Samorodnitsky, Gennady; Taqqu, Murad S. 7 1995 Fonctions aléatoires pluri-temporelles: approximation poissonienne du cas brownien et généralisations. Zbl 0341.60008Mandelbrot, Benoit 7 1975 Horton-Strahler ordering of random binary trees. Zbl 0820.60025Yekutieli, Iddo; Mandelbrot, Benoit B. 6 1994 Les objects fractals. Forme, hasard et dimension. (Fractals. Forme, chance and dimension). 2ème éd. 2ème éd. (Les objects fractals. Forme, hasard et dimension.) Zbl 0995.00503Mandelbrot, Benoit 6 1984 Die fraktale Geometrie der Natur. (The fractal geometry of nature). (Übers. aus dem Engl.: Reinhilt Zähle und Ulrich Zähle. Hrsg. von Ulrich Zähle). Zbl 0652.28002Mandelbrot, Benoît B. 6 1987 Exactly self-similar left-sided multifractals. 2nd rev. and enlarged ed. Zbl 0850.28004Mandelbrot, Benoît B.; Evertsz, Carl J. G. 5 1996 Ensembles de multiplicité aléatoires. Zbl 0135.27106Kahane, J. P.; Mandelbrot, B. 5 1965 Fractals and turbulence: Attractors and dispersion. Zbl 0359.76050Mandelbrot, Benoit B. 5 1977 Contribution à la théorie mathématique des jeux de communication. Zbl 0053.40601Mandelbrot, Benoit 4 1953 Peano-Pólya motions, when time is intrinsic or binomial (uniform or multifractal). Zbl 0922.28006Mandelbrot, Benoît B.; Jaffard, Stéphane 4 1997 Comments on: ’A subordinated stochastic process model with finite variance for speculative prices’, by Peter K. Clark. Zbl 0308.90012Mandelbrot, Benoit B. 4 1973 Fractals, graphics, and mathematics education. Foreword by Lynn Arthur Steen. Zbl 1007.00010 3 2002 Negative dimensions and Hölders, multifractals and their Hölder spectra, and the role of lateral preasymptotics in science. Zbl 0887.28004Mandelbrot, Benoît B. 3 1995 Introduction to fractal sums of pulses. Zbl 0829.60032Mandelbrot, Benoît B. 3 1995 On fractal geometry, and a few of the mathematical questions it has raised. Zbl 0562.01012Mandelbrot, Benoit B. 3 1984 Structure of language and its mathematical aspects. Zbl 0111.16102 3 1961 New methods in statistical economics. Zbl 0121.15105Mandelbrot, B. 3 1964 Sporadic random functions and conditional spectral analysis: Self-similar examples and limits. Zbl 0189.18302Mandelbrot, B. 3 1967 Universality and fractals. (Universalités et fractales. Jeux d’enfant ou délits d’initié? Préface de Benoît Mandelbrot.) Zbl 1006.00004Sapoval, Bernard 3 1997 The inescapable need for fractal tools in finance. Zbl 1233.91345Mandelbrot, Benoit B. 3 2005 Self-similarity of the branching structure in very large DLA clusters and other branching fractals. Zbl 0820.60024Yekutieli, Iddo; Mandelbrot, Benoit B.; Kaufman, Henry 2 1994 Topics on fractals in mathematics and physics. Zbl 0997.28004Mandelbrot, Benoit B. 2 2001 Antipodal correlations and the texture (fractal lacunarity) in critical percolation clusters. Zbl 0843.58112Mandelbrot, Benoît B.; Stauffer, Dietrich 2 1994 Simple games of strategy occurring in communication through natural languages. Zbl 0059.13802Mandelbrot, Benoit 2 1954 Colliers aléatoires et une alternative aux promenades au hasard sans boucle: les cordonnets discrets et fractals. Zbl 0386.60049Mandelbrot, Benoit 2 1978 A primer of negative test dimensions and degrees of emptiness for latent sets. Zbl 1168.28005Mandelbrot, Benoit B.; Frame, Michael 2 2009 Scaling in financial prices. I: Tails and dependence. Zbl 1405.91751Mandelbrot, B. B. 2 2001 Scaling in financial prices. III: Cartoon Brownian motions in multifractal time. Zbl 1405.91753Mandelbrot, B. B. 2 2001 Directed recursive models for fractal growth. Zbl 0703.58034Mandelbrot, Benoit B.; Vicsek, Tamás 2 1989 Self-similarity and covered neighborhoods of fractals: A random walk test. Zbl 0808.60037Stauffer, D.; Aharony, A.; Mandelbrot, B. B. 1 1993 On the dynamics of iterated maps. IX: Continuous interpolation of the complex discrete map \(z\to \lambda z(1-z),\) and related topics. Zbl 1063.37528Mandelbrot, Benoit B. 1 1985 Easy and natural generation of multifractals: Multiplying harmonics of periodic functions. Zbl 0965.28003Coppens, Marc-Olivier; Mandelbrot, Benoît B. 1 1999 Some mathematical questions arising in fractal geometry. Zbl 0963.37039Mandelbrot, Benoît B. 1 2000 On the dynamics of iterated maps. IV: The notion of ”Normalized radical” R of the M-set, and the fractal dimension of the boundary of R. Zbl 0571.58017Mandelbrot, Benoit B. 1 1985 On the dynamics of iterated maps. V: Conjecture that the boundary of the M-set has a fractal dimensional equal to 2. Zbl 0571.58018Mandelbrot, Benoit B. 1 1985 On the dynamics of iterated maps VIII: The map \(z\to \lambda (z+1/z)\), from linear to planar chaos, and the measurement of chaos. Zbl 0571.28004Mandelbrot, Benoit B. 1 1984 Self-inverse fractals osculated by sigma-discs and the limit sets of inversion groups. Zbl 0609.30045Mandelbrot, Benoit B. 1 1983 Variables et processus stochastiques de Pareto-Lévy, et la répartition des revenus. Zbl 0092.37504Mandelbrot, Benoît 1 1959 Géométrie fractale de la turbulence. Dimension de Hausdorff, dispersion et nature des singularites du mouvement des fluides. Zbl 0372.76044Mandelbrot, Benoit 1 1976 The fractalist. Memoir of a scientific maverick. With an afterword by Michael Frame. Zbl 1270.01017Mandelbrot, Benoît B. 1 2012 Scaling in financial prices. II: Multifractals and the star equation. Zbl 1405.91752Mandelbrot, B. B. 1 2001 Scaling in financial prices. IV: Multifractal concentration. Zbl 1405.91754Mandelbrot, B. B. 1 2001 Parallel cartoons of fractal models of finance. Zbl 1233.91344Mandelbrot, Benoit B. 1 2005 The fractalist. Memoir of a scientific maverick. With an afterword by Michael Frame. Zbl 1270.01017Mandelbrot, Benoît B. 1 2012 Convergence of complex multiplicative cascades. Zbl 1221.60028Barral, Julien; Jin, Xiong; Mandelbrot, Benoît 19 2010 Uniform convergence for complex [0,1]-martingales. Zbl 1208.60035Barral, Julien; Jin, Xiong; Mandelbrot, Benoît 10 2010 Fractional multiplicative processes. Zbl 1201.60035Barral, Julien; Mandelbrot, Benoît 8 2009 A primer of negative test dimensions and degrees of emptiness for latent sets. Zbl 1168.28005Mandelbrot, Benoit B.; Frame, Michael 2 2009 The inescapable need for fractal tools in finance. Zbl 1233.91345Mandelbrot, Benoit B. 3 2005 Parallel cartoons of fractal models of finance. Zbl 1233.91344Mandelbrot, Benoit B. 1 2005 The (mis)behavior of markets. A fractal view of risk, ruin and reward. Zbl 1140.91004Mandelbrot, Benoit B.; Hudson, Richard L. 33 2004 Random multiplicative multifractal measures. II: Non-degeneracy, moments, dimension, and multifractal analysis for random multiplicative measures. Zbl 1117.28007Barral, Julien; Mandelbrot, Benoît B. 17 2004 Fractals and chaos. The Mandelbrot set and beyond. Selecta volume C. With a foreword by P. W. Jones and texts co-authored by C. J. G. Evertsz and M. C. Gutzwiller. Zbl 1076.01037Mandelbrot, Benoit B. 15 2004 Random multiplicative multifractal measures. I: Introduction to infinite products of independent random functions. Zbl 1088.28004Barral, Julien; Mandelbrot, Benoît B. 12 2004 Multifractal power law distributions: Negative and critical dimensions and other “anomalies”, explained by a simple example. Zbl 1026.28007Mandelbrot, Benoit B. 8 2003 Multiperiodic multifractal martingale measures. Zbl 1047.28003Barral, J.; Coppens, M.-O.; Mandelbrot, B. B. 8 2003 Multifractal products of cylindrical pulses. Zbl 1014.60042Barral, Julien; Mandelbrot, Benoît B. 73 2002 Gaussian self-affinity and fractals. Globality, the earth, \(1/f\) noise, and R/S. Selecta (old or new) volume H. With contributions by F. J. Damerau, M. Frame, K. McCamy, J. W. Van Ness, J. R. Wallis, and others. Selected works of Benoit B. Mandelbrot. Zbl 1007.01020Mandelbrot, Benoit B. 34 2002 Fractals, graphics, and mathematics education. Foreword by Lynn Arthur Steen. Zbl 1007.00010 3 2002 Topics on fractals in mathematics and physics. Zbl 0997.28004Mandelbrot, Benoit B. 2 2001 Scaling in financial prices. I: Tails and dependence. Zbl 1405.91751Mandelbrot, B. B. 2 2001 Scaling in financial prices. III: Cartoon Brownian motions in multifractal time. Zbl 1405.91753Mandelbrot, B. B. 2 2001 Scaling in financial prices. II: Multifractals and the star equation. Zbl 1405.91752Mandelbrot, B. B. 1 2001 Scaling in financial prices. IV: Multifractal concentration. Zbl 1405.91754Mandelbrot, B. B. 1 2001 Some mathematical questions arising in fractal geometry. Zbl 0963.37039Mandelbrot, Benoît B. 1 2000 Multifractals and 1/f noise. Wild self-affinity in physics (1963–1976). Selecta volume. Zbl 0956.28005Mandelbrot, Benoît B. 38 1999 The canopy and shortest path in a self-contacting fractal tree. Zbl 1052.28500Mandelbrot, Benoit B.; Frame, Michael 10 1999 Easy and natural generation of multifractals: Multiplying harmonics of periodic functions. Zbl 0965.28003Coppens, Marc-Olivier; Mandelbrot, Benoît B. 1 1999 Exceptions to the multifractal formalism for discontinuous measures. Zbl 0892.28008Riedi, Rudolph H.; Mandelbrot, Benoît B. 11 1998 Fractals and scaling in finance. Discontinuity, concentration, risk. Zbl 1005.91001Mandelbrot, Benoit B. 178 1997 Inversion formula for continuous multifractals. Zbl 0892.28007Riedi, Rudolf H.; Mandelbrot, Benoît B. 9 1997 Inverse measures, the inversion formula, and discontinuous multifractals. Zbl 0870.28004Mandelbrot, Benoît B.; Riedi, Rudolf H. 8 1997 Peano-Pólya motions, when time is intrinsic or binomial (uniform or multifractal). Zbl 0922.28006Mandelbrot, Benoît B.; Jaffard, Stéphane 4 1997 Universality and fractals. (Universalités et fractales. Jeux d’enfant ou délits d’initié? Préface de Benoît Mandelbrot.) Zbl 1006.00004Sapoval, Bernard 3 1997 Alternative micropulses and fractional Brownian motion. Zbl 0879.60076Cioczek-Georges, R.; Mandelbrot, Benoît B. 25 1996 Local regularity of nonsmooth wavelet expansions and application to the Polya function. Zbl 0916.42024Jaffard, Stéphane; Mandelbrot, Benoît B. 16 1996 Exactly self-similar left-sided multifractals. 2nd rev. and enlarged ed. Zbl 0850.28004Mandelbrot, Benoît B.; Evertsz, Carl J. G. 5 1996 A class of micropulses and antipersistent fractional Brownian motion. Zbl 0846.60055Cioczek-Georges, Renata; Mandelbrot, Benoît B. 36 1995 Multifractal formalism for infinite multinomial measures. Zbl 0866.28005Riedi, Rudolf H.; Mandelbrot, Benoît B. 14 1995 Abraham Robinson. The creation of nonstandard analysis, a personal and mathematical odyssey. With a foreword by Benoit B. Mandelbrot. Zbl 0933.01025Dauben, Joseph Warren 13 1995 Measures of fractal lacunarity: Minkowski content and alternatives. Zbl 0841.28010Mandelbrot, Benoît B. 12 1995 Stable fractal sums of pulses: The cylindrical case. Zbl 0844.60017Cioczek-Georges, Renata; Mandelbrot, Benoît B.; Samorodnitsky, Gennady; Taqqu, Murad S. 7 1995 Negative dimensions and Hölders, multifractals and their Hölder spectra, and the role of lateral preasymptotics in science. Zbl 0887.28004Mandelbrot, Benoît B. 3 1995 Introduction to fractal sums of pulses. Zbl 0829.60032Mandelbrot, Benoît B. 3 1995 Responses to “Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics”, by A. Jaffe and F. Quinn. Zbl 0803.01014Atiyah, Michael; Borel, Armand; Chaitin, G. J.; Friedan, Daniel; Glimm, James; Gray, Jeremy J.; Hirsch, Morris W.; MacLane, Saunders; Mandelbrot, Benoit B.; Ruelle, David; Schwarz, Albert; Uhlenbeck, Karen; Thom, René; Witten, Edward; Zeeman, Christopher 9 1994 Horton-Strahler ordering of random binary trees. Zbl 0820.60025Yekutieli, Iddo; Mandelbrot, Benoit B. 6 1994 Self-similarity of the branching structure in very large DLA clusters and other branching fractals. Zbl 0820.60024Yekutieli, Iddo; Mandelbrot, Benoit B.; Kaufman, Henry 2 1994 Antipodal correlations and the texture (fractal lacunarity) in critical percolation clusters. Zbl 0843.58112Mandelbrot, Benoît B.; Stauffer, Dietrich 2 1994 Self-similarity and covered neighborhoods of fractals: A random walk test. Zbl 0808.60037Stauffer, D.; Aharony, A.; Mandelbrot, B. B. 1 1993 The fractal geometry of nature. Sonderausgabe. (Die fraktale Geometrie der Natur. Übers. aus dem Englischen von Reinhilt Zähle und Ulrich Zähle.) Zbl 0925.28001Mandelbrot, Benoît B. 51 1991 Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism. Zbl 0850.76277Mandelbrot, Benoît B. 11 1991 Negative fractal dimensions and multifractals. Zbl 0713.58034Mandelbrot, Benoit B. 23 1990 Fractal geometry: What is it, and what does it do! Zbl 0746.00012Mandelbrot, B. B. 24 1989 Directed recursive models for fractal growth. Zbl 0703.58034Mandelbrot, Benoit B.; Vicsek, Tamás 2 1989 The science of fractal images. With contributions by Yuval Fisher and Michael McGuire. Ed. by Heinz-Otto Peitgen and Dietmar Saupe. (Based on notes for the course fractals - introduction, basics and pespectives given as part of the SIG-GRAPH ’87, Anaheim, Calif. course program). Zbl 0683.58003Barnsley, Michael F.; Devaney, Robert L.; Mandelbrot, Benoit B.; Peitgen, Heinz-Otto; Saupe, Dietmar; Voss, Richard 20 1988 Die fraktale Geometrie der Natur. (The fractal geometry of nature). (Übers. aus dem Engl.: Reinhilt Zähle und Ulrich Zähle. Hrsg. von Ulrich Zähle). Zbl 0652.28002Mandelbrot, Benoît B. 6 1987 The beauty of fractals. Images of complex dynamical systems. Zbl 0601.58003Peitgen, H.-O.; Richter, P. H. 135 1986 Self-affine fractals and fractal dimension. Zbl 1063.28500Mandelbrot, Benoit B. 31 1985 On the dynamics of iterated maps. IX: Continuous interpolation of the complex discrete map \(z\to \lambda z(1-z),\) and related topics. Zbl 1063.37528Mandelbrot, Benoit B. 1 1985 On the dynamics of iterated maps. IV: The notion of ”Normalized radical” R of the M-set, and the fractal dimension of the boundary of R. Zbl 0571.58017Mandelbrot, Benoit B. 1 1985 On the dynamics of iterated maps. V: Conjecture that the boundary of the M-set has a fractal dimensional equal to 2. Zbl 0571.58018Mandelbrot, Benoit B. 1 1985 Les objects fractals. Forme, hasard et dimension. (Fractals. Forme, chance and dimension). 2ème éd. 2ème éd. (Les objects fractals. Forme, hasard et dimension.) Zbl 0995.00503Mandelbrot, Benoit 6 1984 On fractal geometry, and a few of the mathematical questions it has raised. Zbl 0562.01012Mandelbrot, Benoit B. 3 1984 On the dynamics of iterated maps VIII: The map \(z\to \lambda (z+1/z)\), from linear to planar chaos, and the measurement of chaos. Zbl 0571.28004Mandelbrot, Benoit B. 1 1984 On the quadratic mapping \(z\rightarrow z^{2}-\mu \) for complex \(\mu \) and \(z\): the fractal structure of its set, and scaling. Zbl 1194.30028Mandelbrot, Benoit B. 125 1983 Self-inverse fractals osculated by sigma-discs and the limit sets of inversion groups. Zbl 0609.30045Mandelbrot, Benoit B. 1 1983 The fractal geometry of nature. Rev. ed. of “Fractals”, 1977. Zbl 0504.28001Mandelbrot, Benoit B. 1,162 1982 Fractal aspects of the iteration of \(z \to \lambda z(1-z)\) for complex \(\lambda\) and z. Zbl 0478.58017Mandelbrot, Benoit B. 23 1980 Robust R/S analysis of long-run serial correlation. Zbl 0518.62036Mandelbrot, Benoit B.; Taqqu, Murad S. 34 1979 Colliers aléatoires et une alternative aux promenades au hasard sans boucle: les cordonnets discrets et fractals. Zbl 0386.60049Mandelbrot, Benoit 2 1978 Fractals. Form, chance, and dimension. Translation. Zbl 0376.28020Mandelbrot, Benoit B. 247 1977 Fractals and turbulence: Attractors and dispersion. Zbl 0359.76050Mandelbrot, Benoit B. 5 1977 Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3 + B. Zbl 0372.76043Mandelbrot, Benoit 10 1976 Géométrie fractale de la turbulence. Dimension de Hausdorff, dispersion et nature des singularites du mouvement des fluides. Zbl 0372.76044Mandelbrot, Benoit 1 1976 Fractals. Form, chance and dimension. (Les objets fractals. Forme, hasard et dimension.) Zbl 0900.00018Mandelbrot, Benoît B. 51 1975 Limit theorems on the self normalized range for weakly and strongly dependent processes. Zbl 0288.60033Mandelbrot, Benoit B. 36 1975 On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars. Zbl 0329.76047Mandelbrot, Benoit B. 23 1975 Fonctions aléatoires pluri-temporelles: approximation poissonienne du cas brownien et généralisations. Zbl 0341.60008Mandelbrot, Benoit 7 1975 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. Zbl 0289.76031Mandelbrot, Benoit B. 236 1974 Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire. Zbl 0276.60096Mandelbrot, Benoit 41 1974 Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire: quelques extensions. Zbl 0276.60097Mandelbrot, Benoit 23 1974 A population birth-and-mutation process. I.: Explicit distributions for the number of mutants in an old culture of bacteria. Zbl 0287.60093Mandelbrot, Benoit 12 1974 Comments on: ’A subordinated stochastic process model with finite variance for speculative prices’, by Peter K. Clark. Zbl 0308.90012Mandelbrot, Benoit B. 4 1973 Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence. Zbl 0227.76081Mandelbrot, Benoit B. 47 1972 Renewal sets and random cutouts. Zbl 0234.60102Mandelbrot, Benoit B. 30 1972 On Dvoretzky coverings for the circle. Zbl 0222.60044Mandelbrot, Benoit B. 13 1972 Long-run linearity, locally Gaussian process, H-spectra and infinite variances. Zbl 0191.51002Mandelbrot, B. 27 1969 Fractional Brownian motions, fractional noises and applications. Zbl 0179.47801Mandelbrot, B. B.; Van Ness, J. W. 1,132 1968 Some noises with \(1/f\) spectrum, a bridge between direct current and white noise. Zbl 0148.40507Mandelbrot, Benoit 56 1967 Sporadic random functions and conditional spectral analysis: Self-similar examples and limits. Zbl 0189.18302Mandelbrot, B. 3 1967 Une classe de processus stochastiques homothetiques à soi; application à la loi climatologique de H.E. Hurst. Zbl 0127.09501Mandelbrot, B. 10 1965 Ensembles de multiplicité aléatoires. Zbl 0135.27106Kahane, J. P.; Mandelbrot, B. 5 1965 New methods in statistical economics. Zbl 0121.15105Mandelbrot, B. 3 1964 The role of sufficiency and of estimation in thermodynamics. Zbl 0111.33705Mandelbrot, B. 14 1962 Sur certains prix spéculatifs: faits empiriques et modèle basé sur les processus stables additifs non gaussiens de Paul Lévy. Zbl 0100.34904Mandelbrot, Benoit 9 1962 Stable paretian random functions and the multiplicative variation of income. Zbl 0104.38402Mandelbrot, Benoit 10 1961 Structure of language and its mathematical aspects. Zbl 0111.16102 3 1961 The Pareto-Lévy law and the distribution of income. Zbl 0201.51101Mandelbrot, B. 73 1960 A note on a class of skew distribution functions: Analysis and critique of a paper by H. A. Simon. Zbl 0101.11303Mandelbrot, Benoit 8 1959 Variables et processus stochastiques de Pareto-Lévy, et la répartition des revenus. Zbl 0092.37504Mandelbrot, Benoît 1 1959 Simple games of strategy occurring in communication through natural languages. Zbl 0059.13802Mandelbrot, Benoit 2 1954 Contribution à la théorie mathématique des jeux de communication. Zbl 0053.40601Mandelbrot, Benoit 4 1953 all cited Publications top 5 cited Publications all top 5 Cited by 5,150 Authors 33 Jumarie, Guy M. 30 Barral, Julien 24 Anh, Vo V. 24 Taqqu, Murad S. 23 Mandelbrot, Benoit B. 20 Li, Ming 17 Luo, Shaokai 16 Seuret, Stéphane 15 Eliazar, Iddo I. 14 Chen, Yangquan 14 Nualart, David 14 Shang, Pengjian 14 Vargas, Vincent 14 Wang, Jun 13 Abry, Patrice 13 Deng, Weihua 13 Falconer, Kenneth J. 13 Jaffard, Stéphane 13 Wang, Xingyuan 12 Băleanu, Dumitru I. 12 Leonenko, Nikolai N. 12 Rhodes, Rémi 12 Ruiz-Medina, María Dolores 12 Wyłomańska, Agnieszka 11 Angulo, José Miguel 11 Ben Slimane, Mourad 11 Chand, Arya Kumar Bedabrata 11 Chen, Yanguang 11 Muzy, Jean-François 10 Bacry, Emmanuel 10 Cattani, Carlo 10 Jin, Xiong 10 Navascués, María Antonia 10 West, Bruce J. 9 Chechkin, Aleksei V. 9 Fernández Martínez, Manuel 9 Grigolini, Paolo 9 Hu, Yaozhong 9 Lapidus, Michel L. 9 Liu, Shutang 9 Ostrovskii, Dmitrii M. 9 Romera, Miguel 9 Warma, Mahamadi 9 Werner, Wendelin 9 Xu, Yanli 8 Balankin, Alexander S. 8 Coeurjolly, Jean-François 8 Lacaux, Céline 8 Lai, Dejian 8 Meerschaert, Mark Marvin 8 Montoya, Fausto 8 Ostoja-Starzewski, Martin 8 Ouknine, Youssef 8 Pastor, Gerardo 8 Sánchez Granero, Miguel Ángel 8 Shen, Guangjun 8 Sornette, Didier 8 Wendt, Herwig 8 Xu, Yong 8 Zhao, Wei 7 Ahmed, Hamdy M. 7 Arneodo, Alain 7 Cohen, Serge 7 Didier, Gustavo 7 Duplantier, Bertrand 7 Feng, De-Jun 7 He, Jinman 7 Huang, Zhiyuan 7 Huillet, Thierry E. 7 Lévy Véhel, Jacques 7 Liu, Quansheng 7 Maslov, Viktor Pavlovich 7 Maslowski, Bohdan 7 McKibben, Mark Anthony 7 Mehrdoust, Farshid 7 Metzler, Ralf 7 Nottale, Laurent 7 Øksendal, Bernt Karsten 7 Panagiotopoulos, Panagiotis D. 7 Pei, Bin 7 Peyrière, Jacques 7 Rachev, Svetlozar T. 7 Saksman, Eero 7 Sikora, Grzegorz 7 Suomala, Ville 7 Yu, Boming 7 Zhang, Xiaotian 7 Zunino, Luciano 6 Barnsley, Michael Fielding 6 Biermé, Hermine 6 Carpinteri, Alberto 6 Duc, Luu Hoang 6 Fyodorov, Yan V. 6 Garcin, Matthieu 6 Gdawiec, Krzysztof 6 Golmankhaneh, Alireza Khalili 6 Kurths, Jürgen 6 Lakhel, El Hassan 6 Lawler, Gregory Francis 6 Machado, José António Tenreiro ...and 5,050 more Authors all top 5 Cited in 565 Serials 268 Chaos, Solitons and Fractals 203 Physica A 107 Fractals 101 Journal of Statistical Physics 86 Physica D 72 Stochastic Processes and their Applications 57 Physics Letters. A 56 Statistics & Probability Letters 49 Chaos 42 Communications in Nonlinear Science and Numerical Simulation 40 Applied Mathematics and Computation 36 Communications in Mathematical Physics 35 Stochastic Analysis and Applications 33 Journal of Mathematical Analysis and Applications 33 Journal of Econometrics 33 Journal of Theoretical Probability 32 Journal of Fluid Mechanics 29 Mathematical Problems in Engineering 27 Journal of Mathematical Physics 27 The Annals of Probability 27 Mathematical and Computer Modelling 27 Quantitative Finance 26 Probability Theory and Related Fields 25 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 23 Computers & Mathematics with Applications 23 Advances in Mathematics 23 The Annals of Applied Probability 23 Bernoulli 23 Nonlinear Dynamics 22 Communications in Statistics. Theory and Methods 22 Stochastics and Dynamics 20 Journal of Computational and Applied Mathematics 20 Computational Statistics and Data Analysis 20 Fractional Calculus & Applied Analysis 19 International Journal of Theoretical Physics 19 Discrete Dynamics in Nature and Society 19 Advances in Difference Equations 19 Stochastics 18 Advances in Applied Probability 18 Journal of Statistical Planning and Inference 17 Transactions of the American Mathematical Society 17 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 17 Journal of Time Series Analysis 17 Applied Mathematical Modelling 16 Journal of Statistical Mechanics: Theory and Experiment 15 Journal of Computational Physics 15 Journal of the Franklin Institute 15 The Annals of Statistics 15 Journal of Physics A: Mathematical and Theoretical 15 Journal of Theoretical Biology 14 The Mathematical Intelligencer 13 Acta Mechanica 13 Mathematical Biosciences 13 Physics Reports 13 Abstract and Applied Analysis 13 Physical Review Letters 13 Comptes Rendus. Mathématique. Académie des Sciences, Paris 12 Applied Mathematics Letters 12 Physics of Fluids 11 Mathematics and Computers in Simulation 11 Theoretical Computer Science 11 Economics Letters 11 Communications in Statistics. Simulation and Computation 11 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 11 Applied and Computational Harmonic Analysis 11 The Journal of Fourier Analysis and Applications 11 Journal of Applied Statistics 11 Econometric Theory 11 The European Physical Journal B. Condensed Matter and Complex Systems 10 Proceedings of the American Mathematical Society 10 Acta Applicandae Mathematicae 10 Applied Numerical Mathematics 10 Pattern Recognition 10 Statistical Inference for Stochastic Processes 9 International Journal of Heat and Mass Transfer 9 Israel Journal of Mathematics 9 Japan Journal of Applied Mathematics 9 Constructive Approximation 9 Econometric Reviews 9 Signal Processing 9 Acta Mathematica Sinica. English Series 8 International Journal of Engineering Science 8 Theoretical and Mathematical Physics 8 Information Sciences 8 Journal of Applied Probability 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Aequationes Mathematicae 8 Journal of Mathematical Imaging and Vision 8 Electronic Journal of Probability 8 International Journal of Theoretical and Applied Finance 8 Nonlinear Analysis. Real World Applications 8 Annals of Finance 7 International Journal of Modern Physics B 7 Mathematical Notes 7 Physics of Fluids 7 Bulletin of Mathematical Biology 7 Journal of Functional Analysis 7 Monatshefte für Mathematik 7 Annals of Physics 7 Statistical Papers ...and 465 more Serials all top 5 Cited in 59 Fields 1,259 Probability theory and stochastic processes (60-XX) 686 Measure and integration (28-XX) 564 Statistics (62-XX) 456 Dynamical systems and ergodic theory (37-XX) 390 Statistical mechanics, structure of matter (82-XX) 368 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 244 Partial differential equations (35-XX) 240 Numerical analysis (65-XX) 221 Real functions (26-XX) 218 Fluid mechanics (76-XX) 187 Biology and other natural sciences (92-XX) 166 Computer science (68-XX) 148 Ordinary differential equations (34-XX) 124 Information and communication theory, circuits (94-XX) 113 Quantum theory (81-XX) 104 Systems theory; control (93-XX) 97 Harmonic analysis on Euclidean spaces (42-XX) 76 Mechanics of deformable solids (74-XX) 70 Geophysics (86-XX) 69 Number theory (11-XX) 66 Functions of a complex variable (30-XX) 56 Combinatorics (05-XX) 55 Operator theory (47-XX) 46 Operations research, mathematical programming (90-XX) 44 Relativity and gravitational theory (83-XX) 41 General topology (54-XX) 37 Mechanics of particles and systems (70-XX) 36 General and overarching topics; collections (00-XX) 34 Functional analysis (46-XX) 33 Classical thermodynamics, heat transfer (80-XX) 30 Approximations and expansions (41-XX) 29 Difference and functional equations (39-XX) 29 Integral equations (45-XX) 29 Global analysis, analysis on manifolds (58-XX) 28 Special functions (33-XX) 27 Calculus of variations and optimal control; optimization (49-XX) 25 Convex and discrete geometry (52-XX) 20 History and biography (01-XX) 20 Integral transforms, operational calculus (44-XX) 19 Differential geometry (53-XX) 16 Astronomy and astrophysics (85-XX) 15 Mathematical logic and foundations (03-XX) 15 Optics, electromagnetic theory (78-XX) 12 Group theory and generalizations (20-XX) 10 Manifolds and cell complexes (57-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 7 Potential theory (31-XX) 7 Geometry (51-XX) 7 Algebraic topology (55-XX) 6 Abstract harmonic analysis (43-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Sequences, series, summability (40-XX) 2 Algebraic geometry (14-XX) 2 Category theory; homological algebra (18-XX) 2 Mathematics education (97-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Topological groups, Lie groups (22-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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