Edit Profile (opens in new tab) Mandelbrot, Benoit B. (b. 1924 d. 2010) Co-Author Distance 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: 121 Publications since 1951, including 16 Books and 1 Additional arXiv Preprint 3 Contributions as Editor · 4 Further Contributions Biographic References: 50 Publications Co-Authors: 40 Co-Authors with 41 Joint Publications 1,478 Co-Co-Authors all top 5 Co-Authors 83 single-authored 8 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 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 62 Measure and integration (28-XX) 41 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) 12 Functions of a complex variable (30-XX) 11 Fluid mechanics (76-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 103 Publications have been cited 5,232 times in 4,286 Documents Cited by ▼ Year ▼ Fractional Brownian motions, fractional noises and applications. Zbl 0179.47801 Mandelbrot, B. B.; Van Ness, J. W. 1,408 1968 The fractal geometry of nature. Rev. ed. of “Fractals”, 1977. Zbl 0504.28001 Mandelbrot, Benoit B. 1,396 1982 Fractals. Form, chance, and dimension. Translation. Zbl 0376.28020 Mandelbrot, Benoit B. 295 1977 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. Zbl 0289.76031 Mandelbrot, Benoit B. 276 1974 Fractals and scaling in finance. Discontinuity, concentration, risk. Zbl 1005.91001 Mandelbrot, Benoit B. 235 1997 On the quadratic mapping \(z\rightarrow z^{2}-\mu \) for complex \(\mu \) and \(z\): the fractal structure of its set, and scaling. Zbl 1194.30028 Mandelbrot, Benoit B. 155 1983 The beauty of fractals. Images of complex dynamical systems. Zbl 0601.58003 Peitgen, H.-O.; Richter, P. H. 153 1986 The Pareto-Lévy law and the distribution of income. Zbl 0201.51101 Mandelbrot, B. 88 1960 Some noises with \(1/f\) spectrum, a bridge between direct current and white noise. Zbl 0148.40507 Mandelbrot, Benoit 78 1967 Multifractal products of cylindrical pulses. Zbl 1014.60042 Barral, Julien; Mandelbrot, Benoît B. 77 2002 Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence. Zbl 0227.76081 Mandelbrot, Benoit B. 62 1972 Fractals. Form, chance and dimension. (Les objets fractals. Forme, hasard et dimension.) Zbl 0900.00018 Mandelbrot, Benoît B. 57 1975 The fractal geometry of nature. Sonderausgabe. (Die fraktale Geometrie der Natur. Übers. aus dem Englischen von Reinhilt Zähle und Ulrich Zähle.) Zbl 0925.28001 Mandelbrot, Benoît B. 53 1991 Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire. Zbl 0276.60096 Mandelbrot, Benoit 45 1974 Multifractals and 1/f noise. Wild self-affinity in physics (1963–1976). Selecta volume. Zbl 0956.28005 Mandelbrot, Benoît B. 41 1999 The (mis)behavior of markets. A fractal view of risk, ruin and reward. Zbl 1140.91004 Mandelbrot, Benoit B.; Hudson, Richard L. 41 2004 Limit theorems on the self normalized range for weakly and strongly dependent processes. Zbl 0288.60033 Mandelbrot, Benoit B. 40 1975 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 0683.58003 Barnsley, Michael F.; Devaney, Robert L.; Mandelbrot, Benoit B.; Peitgen, Heinz-Otto; Saupe, Dietmar; Voss, Richard 39 1988 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 1007.01020 Mandelbrot, Benoit B. 39 2002 A class of micropulses and antipersistent fractional Brownian motion. Zbl 0846.60055 Cioczek-Georges, Renata; Mandelbrot, Benoît B. 38 1995 Robust R/S analysis of long-run serial correlation. Zbl 0518.62036 Mandelbrot, Benoit B.; Taqqu, Murad S. 35 1979 Self-affine fractals and fractal dimension. Zbl 1063.28500 Mandelbrot, Benoit B. 33 1985 Long-run linearity, locally Gaussian process, H-spectra and infinite variances. Zbl 0191.51002 Mandelbrot, B. 32 1969 Renewal sets and random cutouts. Zbl 0234.60102 Mandelbrot, Benoit B. 31 1972 Fractal aspects of the iteration of \(z \to \lambda z(1-z)\) for complex \(\lambda\) and z. Zbl 0478.58017 Mandelbrot, Benoit B. 31 1980 Negative fractal dimensions and multifractals. Zbl 0713.58034 Mandelbrot, Benoit B. 28 1990 Alternative micropulses and fractional Brownian motion. Zbl 0879.60076 Cioczek-Georges, R.; Mandelbrot, Benoît B. 27 1996 Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire: quelques extensions. Zbl 0276.60097 Mandelbrot, Benoit 27 1974 Structure of language and its mathematical aspects. Zbl 0111.16102 27 1961 Fractal geometry: What is it, and what does it do! Zbl 0746.00012 Mandelbrot, B. B. 26 1989 On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars. Zbl 0329.76047 Mandelbrot, Benoit B. 26 1975 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 1076.01037 Mandelbrot, Benoit B. 24 2004 Convergence of complex multiplicative cascades. Zbl 1221.60028 Barral, Julien; Jin, Xiong; Mandelbrot, Benoît 21 2010 The role of sufficiency and of estimation in thermodynamics. Zbl 0111.33705 Mandelbrot, B. 19 1962 Random multiplicative multifractal measures. II: Non-degeneracy, moments, dimension, and multifractal analysis for random multiplicative measures. Zbl 1117.28007 Barral, Julien; Mandelbrot, Benoît B. 19 2004 Multifractal formalism for infinite multinomial measures. Zbl 0866.28005 Riedi, Rudolf H.; Mandelbrot, Benoît B. 18 1995 Local regularity of nonsmooth wavelet expansions and application to the Polya function. Zbl 0916.42024 Jaffard, Stéphane; Mandelbrot, Benoît B. 17 1996 Une classe de processus stochastiques homothetiques à soi; application à la loi climatologique de H.E. Hurst. Zbl 0127.09501 Mandelbrot, B. 17 1965 Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3 + B. Zbl 0372.76043 Mandelbrot, Benoit 15 1976 Responses to “Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics”, by A. Jaffe and F. Quinn. Zbl 0803.01014 Atiyah, 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 15 1994 Abraham Robinson. The creation of nonstandard analysis, a personal and mathematical odyssey. With a foreword by Benoit B. Mandelbrot. Zbl 0933.01025 Dauben, Joseph Warren 15 1995 Measures of fractal lacunarity: Minkowski content and alternatives. Zbl 0841.28010 Mandelbrot, Benoît B. 14 1995 On Dvoretzky coverings for the circle. Zbl 0222.60044 Mandelbrot, Benoit B. 14 1972 Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism. Zbl 0850.76277 Mandelbrot, Benoît B. 13 1991 A population birth-and-mutation process. I.: Explicit distributions for the number of mutants in an old culture of bacteria. Zbl 0287.60093 Mandelbrot, Benoit 13 1974 Random multiplicative multifractal measures. I: Introduction to infinite products of independent random functions. Zbl 1088.28004 Barral, Julien; Mandelbrot, Benoît B. 13 2004 Stable paretian random functions and the multiplicative variation of income. Zbl 0104.38402 Mandelbrot, Benoit 12 1961 The canopy and shortest path in a self-contacting fractal tree. Zbl 1052.28500 Mandelbrot, Benoit B.; Frame, Michael 11 1999 Exceptions to the multifractal formalism for discontinuous measures. Zbl 0892.28008 Riedi, Rudolf H.; Mandelbrot, Benoît B. 11 1998 Uniform convergence for complex [0,1]-martingales. Zbl 1208.60035 Barral, Julien; Jin, Xiong; Mandelbrot, Benoît 11 2010 Multifractal power law distributions: Negative and critical dimensions and other “anomalies”, explained by a simple example. Zbl 1026.28007 Mandelbrot, Benoit B. 10 2003 Inversion formula for continuous multifractals. Zbl 0892.28007 Riedi, Rudolf H.; Mandelbrot, Benoît B. 9 1997 Les objects fractals. Forme, hasard et dimension. (Fractals. Forme, chance and dimension). 2ème éd. 2ème éd. (Les objects fractals. Forme, hasard et dimension.) Zbl 0995.00503 Mandelbrot, Benoit 9 1984 Sur certains prix spéculatifs: faits empiriques et modèle basé sur les processus stables additifs non gaussiens de Paul Lévy. Zbl 0100.34904 Mandelbrot, Benoit 9 1962 Stable fractal sums of pulses: The cylindrical case. Zbl 0844.60017 Cioczek-Georges, Renata; Mandelbrot, Benoît B.; Samorodnitsky, Gennady; Taqqu, Murad S. 8 1995 Inverse measures, the inversion formula, and discontinuous multifractals. Zbl 0870.28004 Mandelbrot, Benoît B.; Riedi, Rudolf H. 8 1997 Multiperiodic multifractal martingale measures. Zbl 1047.28003 Barral, J.; Coppens, M.-O.; Mandelbrot, B. B. 8 2003 Fractional multiplicative processes. Zbl 1201.60035 Barral, Julien; Mandelbrot, Benoît 8 2009 Fonctions aléatoires pluri-temporelles: approximation poissonienne du cas brownien et généralisations. Zbl 0341.60008 Mandelbrot, Benoit 8 1975 A note on a class of skew distribution functions: Analysis and critique of a paper by H. A. Simon. Zbl 0101.11303 Mandelbrot, Benoit 8 1959 Horton-Strahler ordering of random binary trees. Zbl 0820.60025 Yekutieli, Iddo; Mandelbrot, Benoit B. 6 1994 Fractals and turbulence: Attractors and dispersion. Zbl 0359.76050 Mandelbrot, Benoit B. 6 1977 Die fraktale Geometrie der Natur. (The fractal geometry of nature). (Übers. aus dem Engl.: Reinhilt Zähle und Ulrich Zähle. Hrsg. von Ulrich Zähle). Zbl 0652.28002 Mandelbrot, Benoît B. 6 1987 Exactly self-similar left-sided multifractals. Zbl 0850.28004 Mandelbrot, Benoît B.; Evertsz, Carl J. G. 5 1996 Comments on: ’A subordinated stochastic process model with finite variance for speculative prices’, by Peter K. Clark. Zbl 0308.90012 Mandelbrot, Benoit B. 5 1973 Ensembles de multiplicité aléatoires. Zbl 0135.27106 Kahane, J. P.; Mandelbrot, B. 5 1965 Fractals, graphics, and mathematics education. Foreword by Lynn Arthur Steen. Zbl 1007.00010 5 2002 Introduction to fractal sums of pulses. Zbl 0829.60032 Mandelbrot, Benoît B. 4 1995 Peano-Pólya motions, when time is intrinsic or binomial (uniform or multifractal). Zbl 0922.28006 Mandelbrot, Benoît B.; Jaffard, Stéphane 4 1997 Contribution à la théorie mathématique des jeux de communication. Zbl 0053.40601 Mandelbrot, Benoit 4 1953 The inescapable need for fractal tools in finance. Zbl 1233.91345 Mandelbrot, Benoit B. 4 2005 Self-similarity of the branching structure in very large DLA clusters and other branching fractals. Zbl 0820.60024 Yekutieli, Iddo; Mandelbrot, Benoit B.; Kaufman, Henry 3 1994 Negative dimensions and Hölders, multifractals and their Hölder spectra, and the role of lateral preasymptotics in science. Zbl 0887.28004 Mandelbrot, Benoît B. 3 1995 Universality and fractals. (Universalités et fractales. Jeux d’enfant ou délits d’initié? Préface de Benoît Mandelbrot.) Zbl 1006.00004 Sapoval, Bernard 3 1997 A primer of negative test dimensions and degrees of emptiness for latent sets. Zbl 1168.28005 Mandelbrot, Benoit B.; Frame, Michael 3 2009 Scaling in financial prices. I: Tails and dependence. Zbl 1405.91751 Mandelbrot, B. B. 3 2001 Simple games of strategy occurring in communication through natural languages. Zbl 0059.13802 Mandelbrot, Benoit 3 1954 New methods in statistical economics. Zbl 0121.15105 Mandelbrot, B. 3 1964 On fractal geometry, and a few of the mathematical questions it has raised. Zbl 0562.01012 Mandelbrot, Benoit B. 3 1984 Sporadic random functions and conditional spectral analysis: Self-similar examples and limits. Zbl 0189.18302 Mandelbrot, B. 3 1967 Colliers aléatoires et une alternative aux promenades au hasard sans boucle: les cordonnets discrets et fractals. Zbl 0386.60049 Mandelbrot, Benoit 2 1978 Antipodal correlations and the texture (fractal lacunarity) in critical percolation clusters. Zbl 0843.58112 Mandelbrot, Benoît B.; Stauffer, Dietrich 2 1994 Easy and natural generation of multifractals: Multiplying harmonics of periodic functions. Zbl 0965.28003 Coppens, Marc-Olivier; Mandelbrot, Benoît B. 2 1999 Topics on fractals in mathematics and physics. Zbl 0997.28004 Mandelbrot, Benoit B. 2 2001 Scaling in financial prices. III: Cartoon Brownian motions in multifractal time. Zbl 1405.91753 Mandelbrot, B. B. 2 2001 Scaling in financial prices. IV: Multifractal concentration. Zbl 1405.91754 Mandelbrot, B. B. 2 2001 Directed recursive models for fractal growth. Zbl 0703.58034 Mandelbrot, Benoit B.; Vicsek, Tamás 2 1989 Behaviour of the harmonic measure at the bottom of fjords. Zbl 0731.58046 Evertsz, Carl J. G.; Jones, Peter W.; Mandelbrot, Benoit B. 2 1991 Parallel cartoons of fractal models of finance. Zbl 1233.91344 Mandelbrot, Benoit B. 2 2005 The fractalist. Memoir of a scientific maverick. With an afterword by Michael Frame. Zbl 1270.01017 Mandelbrot, Benoît B. 2 2012 Géométrie fractale de la turbulence. Dimension de Hausdorff, dispersion et nature des singularites du mouvement des fluides. Zbl 0372.76044 Mandelbrot, Benoit 1 1976 Self-similarity and covered neighborhoods of fractals: A random walk test. Zbl 0808.60037 Stauffer, D.; Aharony, A.; Mandelbrot, B. B. 1 1993 Scaling in financial prices. II: Multifractals and the star equation. Zbl 1405.91752 Mandelbrot, B. B. 1 2001 Stochastic volatility, power laws and long memory. Zbl 1405.91720 Mandelbrot, B. B. 1 2001 Variables et processus stochastiques de Pareto-Lévy, et la répartition des revenus. Zbl 0092.37504 Mandelbrot, Benoît 1 1959 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 0571.28004 Mandelbrot, Benoit B. 1 1984 Self-inverse fractals osculated by sigma-discs and the limit sets of inversion groups. Zbl 0609.30045 Mandelbrot, Benoit B. 1 1983 On the dynamics of iterated maps. IX: Continuous interpolation of the complex discrete map \(z\to \lambda z(1-z),\) and related topics. Zbl 1063.37528 Mandelbrot, Benoit B. 1 1985 Souvenirs à batons rompus de Szolem Mandelbrojt, recueillis en 1970 et préparés par Benoît Mandelbrot. Zbl 0548.01020 Mandelbrot, Benoît 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 0571.58017 Mandelbrot, Benoit B. 1 1985 The fractalist. Memoir of a scientific maverick. With an afterword by Michael Frame. Zbl 1270.01017 Mandelbrot, Benoît B. 2 2012 Convergence of complex multiplicative cascades. Zbl 1221.60028 Barral, Julien; Jin, Xiong; Mandelbrot, Benoît 21 2010 Uniform convergence for complex [0,1]-martingales. Zbl 1208.60035 Barral, Julien; Jin, Xiong; Mandelbrot, Benoît 11 2010 Fractional multiplicative processes. Zbl 1201.60035 Barral, Julien; Mandelbrot, Benoît 8 2009 A primer of negative test dimensions and degrees of emptiness for latent sets. Zbl 1168.28005 Mandelbrot, Benoit B.; Frame, Michael 3 2009 The inescapable need for fractal tools in finance. Zbl 1233.91345 Mandelbrot, Benoit B. 4 2005 Parallel cartoons of fractal models of finance. Zbl 1233.91344 Mandelbrot, Benoit B. 2 2005 The (mis)behavior of markets. A fractal view of risk, ruin and reward. Zbl 1140.91004 Mandelbrot, Benoit B.; Hudson, Richard L. 41 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 1076.01037 Mandelbrot, Benoit B. 24 2004 Random multiplicative multifractal measures. II: Non-degeneracy, moments, dimension, and multifractal analysis for random multiplicative measures. Zbl 1117.28007 Barral, Julien; Mandelbrot, Benoît B. 19 2004 Random multiplicative multifractal measures. I: Introduction to infinite products of independent random functions. Zbl 1088.28004 Barral, Julien; Mandelbrot, Benoît B. 13 2004 Multifractal power law distributions: Negative and critical dimensions and other “anomalies”, explained by a simple example. Zbl 1026.28007 Mandelbrot, Benoit B. 10 2003 Multiperiodic multifractal martingale measures. Zbl 1047.28003 Barral, J.; Coppens, M.-O.; Mandelbrot, B. B. 8 2003 Multifractal products of cylindrical pulses. Zbl 1014.60042 Barral, Julien; Mandelbrot, Benoît B. 77 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 1007.01020 Mandelbrot, Benoit B. 39 2002 Fractals, graphics, and mathematics education. Foreword by Lynn Arthur Steen. Zbl 1007.00010 5 2002 Scaling in financial prices. I: Tails and dependence. Zbl 1405.91751 Mandelbrot, B. B. 3 2001 Topics on fractals in mathematics and physics. Zbl 0997.28004 Mandelbrot, Benoit B. 2 2001 Scaling in financial prices. III: Cartoon Brownian motions in multifractal time. Zbl 1405.91753 Mandelbrot, B. B. 2 2001 Scaling in financial prices. IV: Multifractal concentration. Zbl 1405.91754 Mandelbrot, B. B. 2 2001 Scaling in financial prices. II: Multifractals and the star equation. Zbl 1405.91752 Mandelbrot, B. B. 1 2001 Stochastic volatility, power laws and long memory. Zbl 1405.91720 Mandelbrot, B. B. 1 2001 Some mathematical questions arising in fractal geometry. Zbl 0963.37039 Mandelbrot, Benoît B. 1 2000 Multifractals and 1/f noise. Wild self-affinity in physics (1963–1976). Selecta volume. Zbl 0956.28005 Mandelbrot, Benoît B. 41 1999 The canopy and shortest path in a self-contacting fractal tree. Zbl 1052.28500 Mandelbrot, Benoit B.; Frame, Michael 11 1999 Easy and natural generation of multifractals: Multiplying harmonics of periodic functions. Zbl 0965.28003 Coppens, Marc-Olivier; Mandelbrot, Benoît B. 2 1999 Exceptions to the multifractal formalism for discontinuous measures. Zbl 0892.28008 Riedi, Rudolf H.; Mandelbrot, Benoît B. 11 1998 Fractals and scaling in finance. Discontinuity, concentration, risk. Zbl 1005.91001 Mandelbrot, Benoit B. 235 1997 Inversion formula for continuous multifractals. Zbl 0892.28007 Riedi, Rudolf H.; Mandelbrot, Benoît B. 9 1997 Inverse measures, the inversion formula, and discontinuous multifractals. Zbl 0870.28004 Mandelbrot, Benoît B.; Riedi, Rudolf H. 8 1997 Peano-Pólya motions, when time is intrinsic or binomial (uniform or multifractal). Zbl 0922.28006 Mandelbrot, Benoît B.; Jaffard, Stéphane 4 1997 Universality and fractals. (Universalités et fractales. Jeux d’enfant ou délits d’initié? Préface de Benoît Mandelbrot.) Zbl 1006.00004 Sapoval, Bernard 3 1997 Alternative micropulses and fractional Brownian motion. Zbl 0879.60076 Cioczek-Georges, R.; Mandelbrot, Benoît B. 27 1996 Local regularity of nonsmooth wavelet expansions and application to the Polya function. Zbl 0916.42024 Jaffard, Stéphane; Mandelbrot, Benoît B. 17 1996 Exactly self-similar left-sided multifractals. Zbl 0850.28004 Mandelbrot, Benoît B.; Evertsz, Carl J. G. 5 1996 A class of micropulses and antipersistent fractional Brownian motion. Zbl 0846.60055 Cioczek-Georges, Renata; Mandelbrot, Benoît B. 38 1995 Multifractal formalism for infinite multinomial measures. Zbl 0866.28005 Riedi, Rudolf H.; Mandelbrot, Benoît B. 18 1995 Abraham Robinson. The creation of nonstandard analysis, a personal and mathematical odyssey. With a foreword by Benoit B. Mandelbrot. Zbl 0933.01025 Dauben, Joseph Warren 15 1995 Measures of fractal lacunarity: Minkowski content and alternatives. Zbl 0841.28010 Mandelbrot, Benoît B. 14 1995 Stable fractal sums of pulses: The cylindrical case. Zbl 0844.60017 Cioczek-Georges, Renata; Mandelbrot, Benoît B.; Samorodnitsky, Gennady; Taqqu, Murad S. 8 1995 Introduction to fractal sums of pulses. Zbl 0829.60032 Mandelbrot, Benoît B. 4 1995 Negative dimensions and Hölders, multifractals and their Hölder spectra, and the role of lateral preasymptotics in science. Zbl 0887.28004 Mandelbrot, Benoît B. 3 1995 Responses to “Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics”, by A. Jaffe and F. Quinn. Zbl 0803.01014 Atiyah, 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 15 1994 Horton-Strahler ordering of random binary trees. Zbl 0820.60025 Yekutieli, Iddo; Mandelbrot, Benoit B. 6 1994 Self-similarity of the branching structure in very large DLA clusters and other branching fractals. Zbl 0820.60024 Yekutieli, Iddo; Mandelbrot, Benoit B.; Kaufman, Henry 3 1994 Antipodal correlations and the texture (fractal lacunarity) in critical percolation clusters. Zbl 0843.58112 Mandelbrot, Benoît B.; Stauffer, Dietrich 2 1994 Self-similarity and covered neighborhoods of fractals: A random walk test. Zbl 0808.60037 Stauffer, 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 0925.28001 Mandelbrot, Benoît B. 53 1991 Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism. Zbl 0850.76277 Mandelbrot, Benoît B. 13 1991 Behaviour of the harmonic measure at the bottom of fjords. Zbl 0731.58046 Evertsz, Carl J. G.; Jones, Peter W.; Mandelbrot, Benoit B. 2 1991 Negative fractal dimensions and multifractals. Zbl 0713.58034 Mandelbrot, Benoit B. 28 1990 Fractal geometry: What is it, and what does it do! Zbl 0746.00012 Mandelbrot, B. B. 26 1989 Directed recursive models for fractal growth. Zbl 0703.58034 Mandelbrot, 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 0683.58003 Barnsley, Michael F.; Devaney, Robert L.; Mandelbrot, Benoit B.; Peitgen, Heinz-Otto; Saupe, Dietmar; Voss, Richard 39 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 0652.28002 Mandelbrot, Benoît B. 6 1987 The beauty of fractals. Images of complex dynamical systems. Zbl 0601.58003 Peitgen, H.-O.; Richter, P. H. 153 1986 Self-affine fractals and fractal dimension. Zbl 1063.28500 Mandelbrot, Benoit B. 33 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 1063.37528 Mandelbrot, Benoit B. 1 1985 Souvenirs à batons rompus de Szolem Mandelbrojt, recueillis en 1970 et préparés par Benoît Mandelbrot. Zbl 0548.01020 Mandelbrot, Benoît 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 0571.58017 Mandelbrot, 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 0571.58018 Mandelbrot, Benoit B. 1 1985 On the dynamics of iterated maps. VII: Domain-filling (”Peano”) sequences for fractal Julia sets, and an intuitive rationale for the Siegel discs. Zbl 0571.58020 Mandelbrot, 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 0995.00503 Mandelbrot, Benoit 9 1984 On fractal geometry, and a few of the mathematical questions it has raised. Zbl 0562.01012 Mandelbrot, 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 0571.28004 Mandelbrot, 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 1194.30028 Mandelbrot, Benoit B. 155 1983 Self-inverse fractals osculated by sigma-discs and the limit sets of inversion groups. Zbl 0609.30045 Mandelbrot, Benoit B. 1 1983 The fractal geometry of nature. Rev. ed. of “Fractals”, 1977. Zbl 0504.28001 Mandelbrot, Benoit B. 1,396 1982 Fractal aspects of the iteration of \(z \to \lambda z(1-z)\) for complex \(\lambda\) and z. Zbl 0478.58017 Mandelbrot, Benoit B. 31 1980 Robust R/S analysis of long-run serial correlation. Zbl 0518.62036 Mandelbrot, Benoit B.; Taqqu, Murad S. 35 1979 Colliers aléatoires et une alternative aux promenades au hasard sans boucle: les cordonnets discrets et fractals. Zbl 0386.60049 Mandelbrot, Benoit 2 1978 Fractals. Form, chance, and dimension. Translation. Zbl 0376.28020 Mandelbrot, Benoit B. 295 1977 Fractals and turbulence: Attractors and dispersion. Zbl 0359.76050 Mandelbrot, Benoit B. 6 1977 Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3 + B. Zbl 0372.76043 Mandelbrot, Benoit 15 1976 Géométrie fractale de la turbulence. Dimension de Hausdorff, dispersion et nature des singularites du mouvement des fluides. Zbl 0372.76044 Mandelbrot, Benoit 1 1976 Fractals. Form, chance and dimension. (Les objets fractals. Forme, hasard et dimension.) Zbl 0900.00018 Mandelbrot, Benoît B. 57 1975 Limit theorems on the self normalized range for weakly and strongly dependent processes. Zbl 0288.60033 Mandelbrot, Benoit B. 40 1975 On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars. Zbl 0329.76047 Mandelbrot, Benoit B. 26 1975 Fonctions aléatoires pluri-temporelles: approximation poissonienne du cas brownien et généralisations. Zbl 0341.60008 Mandelbrot, Benoit 8 1975 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. Zbl 0289.76031 Mandelbrot, Benoit B. 276 1974 Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire. Zbl 0276.60096 Mandelbrot, Benoit 45 1974 Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire: quelques extensions. Zbl 0276.60097 Mandelbrot, Benoit 27 1974 A population birth-and-mutation process. I.: Explicit distributions for the number of mutants in an old culture of bacteria. Zbl 0287.60093 Mandelbrot, Benoit 13 1974 Comments on: ’A subordinated stochastic process model with finite variance for speculative prices’, by Peter K. Clark. Zbl 0308.90012 Mandelbrot, Benoit B. 5 1973 Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence. Zbl 0227.76081 Mandelbrot, Benoit B. 62 1972 Renewal sets and random cutouts. Zbl 0234.60102 Mandelbrot, Benoit B. 31 1972 On Dvoretzky coverings for the circle. Zbl 0222.60044 Mandelbrot, Benoit B. 14 1972 Long-run linearity, locally Gaussian process, H-spectra and infinite variances. Zbl 0191.51002 Mandelbrot, B. 32 1969 Fractional Brownian motions, fractional noises and applications. Zbl 0179.47801 Mandelbrot, B. B.; Van Ness, J. W. 1,408 1968 Some noises with \(1/f\) spectrum, a bridge between direct current and white noise. Zbl 0148.40507 Mandelbrot, Benoit 78 1967 Sporadic random functions and conditional spectral analysis: Self-similar examples and limits. Zbl 0189.18302 Mandelbrot, B. 3 1967 Une classe de processus stochastiques homothetiques à soi; application à la loi climatologique de H.E. Hurst. Zbl 0127.09501 Mandelbrot, B. 17 1965 Ensembles de multiplicité aléatoires. Zbl 0135.27106 Kahane, J. P.; Mandelbrot, B. 5 1965 New methods in statistical economics. Zbl 0121.15105 Mandelbrot, B. 3 1964 The role of sufficiency and of estimation in thermodynamics. Zbl 0111.33705 Mandelbrot, B. 19 1962 Sur certains prix spéculatifs: faits empiriques et modèle basé sur les processus stables additifs non gaussiens de Paul Lévy. Zbl 0100.34904 Mandelbrot, Benoit 9 1962 Structure of language and its mathematical aspects. Zbl 0111.16102 27 1961 Stable paretian random functions and the multiplicative variation of income. Zbl 0104.38402 Mandelbrot, Benoit 12 1961 The Pareto-Lévy law and the distribution of income. Zbl 0201.51101 Mandelbrot, B. 88 1960 A note on a class of skew distribution functions: Analysis and critique of a paper by H. A. Simon. Zbl 0101.11303 Mandelbrot, Benoit 8 1959 ...and 3 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 6,271 Authors 34 Jumarie, Guy M. 31 Barral, Julien 26 Eliazar, Iddo I. 25 Taqqu, Murad S. 24 Anh, Vo V. 23 Mandelbrot, Benoit B. 23 Wyłomańska, Agnieszka 22 Metzler, Ralf 21 Golmankhaneh, Alireza Khalili 21 Li, Ming 20 Chand, Arya Kumar Bedabrata 20 Chechkin, Aleksei V. 18 Seuret, Stéphane 17 Luo, Shaokai 16 Abry, Patrice 16 Deng, Weihua 16 Jaffard, Stéphane 16 Xu, Yong 15 Shang, Pengjian 15 Wang, Xingyuan 14 Băleanu, Dumitru I. 14 Chen, Yangquan 14 Falconer, Kenneth J. 14 Navascués, María Antonia 14 Nualart, David 14 Vargas, Vincent 14 Wang, Jun 12 Leonenko, Nikolai N. 12 Rhodes, Rémi 12 Ruiz-Medina, María Dolores 12 Wang, Xiaotian 12 West, Bruce J. 11 Angulo, José Miguel 11 Ben Slimane, Mourad 11 Chen, Yanguang 11 Jin, Xiong 11 Muzy, Jean-François 11 Ostrovskii, Dmitrii M. 11 Romera, Miguel 10 Bacry, Emmanuel 10 Cattani, Carlo 10 Grigolini, Paolo 10 Liu, Shutang 10 Montoya, Fausto 10 Pastor, Gerardo 10 Shen, Guangjun 10 Warma, Mahamadi 10 Wendt, Herwig 9 Barnsley, Michael Fielding 9 Duc, Luu Hoang 9 Fernández Martínez, Manuel 9 Hu, Yaozhong 9 Lacaux, Céline 9 Lapidus, Michel L. 9 Mathew Karakkad, Sunil 9 Ostoja-Starzewski, Martin 9 Sikora, Grzegorz 9 Werner, Wendelin 9 Xu, Yanli 8 Coeurjolly, Jean-François 8 Didier, Gustavo 8 Duplantier, Bertrand 8 El-Nabulsi, Rami Ahmad 8 Gajda, Janusz 8 Gdawiec, Krzysztof 8 Huillet, Thierry E. 8 Kurths, Jürgen 8 Lai, Dejian 8 Lévy Véhel, Jacques 8 Machado, José António Tenreiro 8 Meerschaert, Mark Marvin 8 Nordman, Daniel J. 8 Ouknine, Youssef 8 Panagiotopoulos, Panagiotis D. 8 Pei, Bin 8 Rachev, Svetlozar T. 8 Saksman, Eero 8 Sánchez Granero, Miguel Ángel 8 Sornette, Didier 8 Yu, Boming 8 Zhao, Wei 8 Zunino, Luciano 7 Ahmed, Hamdy M. 7 Arneodo, Alain 7 Balankin, Alexander S. 7 Bianchi, Sergio 7 Chang, Shu-Chiuan 7 Cohen, Serge 7 Feng, De-Jun 7 Fyodorov, Yan V. 7 Garcin, Matthieu 7 He, Jinman 7 Huang, Zhiyuan 7 Koverda, V. P. 7 Lahiri, Soumendra Nath 7 Lakhel, El Hassan 7 Liu, Quansheng 7 Malomed, Boris A. 7 Maslov, Viktor Pavlovich 7 Maslowski, Bohdan ...and 6,171 more Authors all top 5 Cited in 641 Serials 291 Chaos, Solitons and Fractals 251 Physica A 132 Fractals 112 Physica D 104 Journal of Statistical Physics 82 Physics Letters. 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Series A: Theory and Methods 8 Journal of Mathematical Sciences (New York) 8 Methodology and Computing in Applied Probability 8 Applied Stochastic Models in Business and Industry ...and 541 more Serials all top 5 Cited in 60 Fields 1,518 Probability theory and stochastic processes (60-XX) 839 Measure and integration (28-XX) 692 Statistics (62-XX) 540 Dynamical systems and ergodic theory (37-XX) 471 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 449 Statistical mechanics, structure of matter (82-XX) 327 Partial differential equations (35-XX) 300 Numerical analysis (65-XX) 285 Real functions (26-XX) 262 Fluid mechanics (76-XX) 227 Biology and other natural sciences (92-XX) 206 Computer science (68-XX) 198 Ordinary differential equations (34-XX) 141 Quantum theory (81-XX) 141 Information and communication theory, circuits (94-XX) 118 Systems theory; control (93-XX) 112 Harmonic analysis on Euclidean spaces (42-XX) 88 Mechanics of deformable solids (74-XX) 82 Number theory (11-XX) 82 Geophysics (86-XX) 78 Functions of a complex variable (30-XX) 74 Operator theory (47-XX) 66 Combinatorics (05-XX) 53 Relativity and gravitational theory (83-XX) 53 Operations research, mathematical programming (90-XX) 49 General topology (54-XX) 43 General and overarching topics; collections (00-XX) 43 Mechanics of particles and systems (70-XX) 43 Classical thermodynamics, heat transfer (80-XX) 41 Approximations and expansions (41-XX) 39 Difference and functional equations (39-XX) 39 Functional analysis (46-XX) 36 Special functions (33-XX) 36 Integral equations (45-XX) 34 Global analysis, analysis on manifolds (58-XX) 32 Calculus of variations and optimal control; optimization (49-XX) 28 Convex and discrete geometry (52-XX) 27 History and biography (01-XX) 25 Integral transforms, operational calculus (44-XX) 25 Optics, electromagnetic theory (78-XX) 23 Differential geometry (53-XX) 19 Mathematical logic and foundations (03-XX) 18 Astronomy and astrophysics (85-XX) 15 Group theory and generalizations (20-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 11 Potential theory (31-XX) 11 Manifolds and cell complexes (57-XX) 8 Geometry (51-XX) 8 Algebraic topology (55-XX) 7 Abstract harmonic analysis (43-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Sequences, series, summability (40-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 2 Algebraic geometry (14-XX) 2 Category theory; homological algebra (18-XX) 2 Topological groups, Lie groups (22-XX) 2 Mathematics education (97-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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