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Mandelbrot, Benoit B.

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Published as: Mandelbrot, Benoit B.; Mandelbrot, Benoît B.; Mandelbrot, Benoit; Mandelbrot, Benoît; Mandelbrot, B. B.; Mandelbrot, B.
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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 Salomon
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

Publications by Year

Citations contained in zbMATH Open

99 Publications have been cited 4,305 times in 3,403 Documents Cited by Year
The fractal geometry of nature. Rev. ed. of “Fractals”, 1977. Zbl 0504.28001
Mandelbrot, Benoit B.
1982
Fractional Brownian motions, fractional noises and applications. Zbl 0179.47801
Mandelbrot, B. B.; Van Ness, J. W.
1968
Fractals. Form, chance, and dimension. Translation. Zbl 0376.28020
Mandelbrot, Benoit B.
241
1977
Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. Zbl 0289.76031
Mandelbrot, Benoit B.
228
1974
Fractals and scaling in finance. Discontinuity, concentration, risk. Zbl 1005.91001
Mandelbrot, Benoit B.
175
1997
The beauty of fractals. Images of complex dynamical systems. Zbl 0601.58003
Peitgen, H.-O.; Richter, P. H.
131
1986
On the quadratic mapping \(z\rightarrow z^{2}-\mu \) for complex \(\mu \) and \(z\): the fractal structure of its set, and scaling. Zbl 1194.30028
Mandelbrot, Benoit B.
120
1983
Multifractal products of cylindrical pulses. Zbl 1014.60042
Barral, Julien; Mandelbrot, Benoît B.
70
2002
The Pareto-Lévy law and the distribution of income. Zbl 0201.51101
Mandelbrot, B.
67
1960
Some noises with \(1/f\) spectrum, a bridge between direct current and white noise. Zbl 0148.40507
Mandelbrot, Benoit
55
1967
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.
51
1991
Fractals. Form, chance and dimension. (Les objets fractals. Forme, hasard et dimension.) Zbl 0900.00018
Mandelbrot, Benoît B.
47
1975
Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence. Zbl 0227.76081
Mandelbrot, Benoit B.
46
1972
Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire. Zbl 0276.60096
Mandelbrot, Benoit
41
1974
Multifractals and 1/f noise. Wild self-affinity in physics (1963–1976). Selecta volume. Zbl 0956.28005
Mandelbrot, Benoît B.
38
1999
A class of micropulses and antipersistent fractional Brownian motion. Zbl 0846.60055
Cioczek-Georges, Renata; Mandelbrot, Benoît B.
36
1995
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.
33
2002
Limit theorems on the self normalized range for weakly and strongly dependent processes. Zbl 0288.60033
Mandelbrot, Benoit B.
33
1975
Robust R/S analysis of long-run serial correlation. Zbl 0518.62036
Mandelbrot, Benoit B.; Taqqu, Murad S.
32
1979
The (mis)behavior of markets. A fractal view of risk, ruin and reward. Zbl 1140.91004
Mandelbrot, Benoit B.; Hudson, Richard L.
31
2004
Renewal sets and random cutouts. Zbl 0234.60102
Mandelbrot, Benoit B.
30
1972
Self-affine fractals and fractal dimension. Zbl 1063.28500
Mandelbrot, Benoit B.
28
1985
Long-run linearity, locally Gaussian process, H-spectra and infinite variances. Zbl 0191.51002
Mandelbrot, B.
27
1969
Alternative micropulses and fractional Brownian motion. Zbl 0879.60076
Cioczek-Georges, R.; Mandelbrot, Benoît B.
24
1996
Fractal geometry: What is it, and what does it do! Zbl 0746.00012
Mandelbrot, B. B.
24
1989
Negative fractal dimensions and multifractals. Zbl 0713.58034
Mandelbrot, Benoit B.
23
1990
On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars. Zbl 0329.76047
Mandelbrot, Benoit B.
23
1975
Fractal aspects of the iteration of \(z \to \lambda z(1-z)\) for complex \(\lambda\) and z. Zbl 0478.58017
Mandelbrot, Benoit B.
22
1980
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
20
1988
Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire: quelques extensions. Zbl 0276.60097
Mandelbrot, Benoit
20
1974
Convergence of complex multiplicative cascades. Zbl 1221.60028
Barral, Julien; Jin, Xiong; Mandelbrot, Benoît
18
2010
Random multiplicative multifractal measures. II: Non-degeneracy, moments, dimension, and multifractal analysis for random multiplicative measures. Zbl 1117.28007
Barral, Julien; Mandelbrot, Benoît B.
17
2004
Local regularity of nonsmooth wavelet expansions and application to the Polya function. Zbl 0916.42024
Jaffard, Stéphane; Mandelbrot, Benoît B.
15
1996
Multifractal formalism for infinite multinomial measures. Zbl 0866.28005
Riedi, Rudolf H.; Mandelbrot, Benoît B.
14
1995
The role of sufficiency and of estimation in thermodynamics. Zbl 0111.33705
Mandelbrot, B.
14
1962
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.
14
2004
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
13
1995
On Dvoretzky coverings for the circle. Zbl 0222.60044
Mandelbrot, Benoit B.
13
1972
Random multiplicative multifractal measures. I: Introduction to infinite products of independent random functions. Zbl 1088.28004
Barral, Julien; Mandelbrot, Benoît B.
12
2004
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
12
1974
Measures of fractal lacunarity: Minkowski content and alternatives. Zbl 0841.28010
Mandelbrot, Benoît B.
11
1995
Exceptions to the multifractal formalism for discontinuous measures. Zbl 0892.28008
Riedi, Rudolph H.; Mandelbrot, Benoît B.
11
1998
Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism. Zbl 0850.76277
Mandelbrot, Benoît B.
11
1991
Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3 + B. Zbl 0372.76043
Mandelbrot, Benoit
11
1976
Uniform convergence for complex [0,1]-martingales. Zbl 1208.60035
Barral, Julien; Jin, Xiong; Mandelbrot, Benoît
10
2010
Une classe de processus stochastiques homothetiques à soi; application à la loi climatologique de H.E. Hurst. Zbl 0127.09501
Mandelbrot, B.
10
1965
Inversion formula for continuous multifractals. Zbl 0892.28007
Riedi, Rudolf H.; Mandelbrot, Benoît B.
9
1997
The canopy and shortest path in a self-contacting fractal tree. Zbl 1052.28500
Mandelbrot, Benoit B.; Frame, Michael
9
1999
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
9
1994
Multiperiodic multifractal martingale measures. Zbl 1047.28003
Barral, J.; Coppens, M.-O.; Mandelbrot, B. B.
8
2003
Multifractal power law distributions: Negative and critical dimensions and other “anomalies”, explained by a simple example. Zbl 1026.28007
Mandelbrot, Benoit B.
8
2003
Inverse measures, the inversion formula, and discontinuous multifractals. Zbl 0870.28004
Mandelbrot, Benoît B.; Riedi, Rudolf H.
8
1997
Sur certains prix spéculatifs: faits empiriques et modèle basé sur les processus stables additifs non gaussiens de Paul Lévy. Zbl 0100.34904
Mandelbrot, Benoit
8
1962
Stable paretian random functions and the multiplicative variation of income. Zbl 0104.38402
Mandelbrot, Benoit
8
1961
Fractional multiplicative processes. Zbl 1201.60035
Barral, Julien; Mandelbrot, Benoît
7
2009
Fonctions aléatoires pluri-temporelles: approximation poissonienne du cas brownien et généralisations. Zbl 0341.60008
Mandelbrot, Benoit
7
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
6
1959
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
Horton-Strahler ordering of random binary trees. Zbl 0820.60025
Yekutieli, Iddo; Mandelbrot, Benoit B.
5
1994
Stable fractal sums of pulses: The cylindrical case. Zbl 0844.60017
Cioczek-Georges, Renata; Mandelbrot, Benoît B.; Samorodnitsky, Gennady; Taqqu, Murad S.
5
1995
Exactly self-similar left-sided multifractals. 2nd rev. and enlarged ed. Zbl 0850.28004
Mandelbrot, Benoît B.; Evertsz, Carl J. G.
5
1996
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
5
1984
Ensembles de multiplicité aléatoires. Zbl 0135.27106
Kahane, J. P.; Mandelbrot, B.
5
1965
Fractals and turbulence: Attractors and dispersion. Zbl 0359.76050
Mandelbrot, Benoit B.
5
1977
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
Comments on: ’A subordinated stochastic process model with finite variance for speculative prices’, by Peter K. Clark. Zbl 0308.90012
Mandelbrot, Benoit B.
4
1973
Universality and fractals. (Universalités et fractales. Jeux d’enfant ou délits d’initié? Préface de Benoît Mandelbrot.) Zbl 1006.00004
Sapoval, Bernard
3
1997
Introduction to fractal sums of pulses. Zbl 0829.60032
Mandelbrot, Benoît B.
3
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
Structure of language and its mathematical aspects. Zbl 0111.16102
3
1961
Sporadic random functions and conditional spectral analysis: Self-similar examples and limits. Zbl 0189.18302
Mandelbrot, B.
3
1967
Fractals, graphics, and mathematics education. Foreword by Lynn Arthur Steen. Zbl 1007.00010
3
2002
On fractal geometry, and a few of the mathematical questions it has raised. Zbl 0562.01012
Mandelbrot, Benoit B.
3
1984
New methods in statistical economics. Zbl 0121.15105
Mandelbrot, B.
3
1964
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
2
1994
Antipodal correlations and the texture (fractal lacunarity) in critical percolation clusters. Zbl 0843.58112
Mandelbrot, Benoît B.; Stauffer, Dietrich
2
1994
Topics on fractals in mathematics and physics. Zbl 0997.28004
Mandelbrot, Benoit B.
2
2001
Simple games of strategy occurring in communication through natural languages. Zbl 0059.13802
Mandelbrot, Benoit
2
1954
Directed recursive models for fractal growth. Zbl 0703.58034
Mandelbrot, Benoit B.; Vicsek, Tamás
2
1989
Colliers aléatoires et une alternative aux promenades au hasard sans boucle: les cordonnets discrets et fractals. Zbl 0386.60049
Mandelbrot, Benoit
2
1978
A primer of negative test dimensions and degrees of emptiness for latent sets. Zbl 1168.28005
Mandelbrot, Benoit B.; Frame, Michael
2
2009
The inescapable need for fractal tools in finance. Zbl 1233.91345
Mandelbrot, Benoit B.
2
2005
Scaling in financial prices. I: Tails and dependence. Zbl 1405.91751
Mandelbrot, B. B.
2
2001
Scaling in financial prices. III: Cartoon Brownian motions in multifractal time. Zbl 1405.91753
Mandelbrot, B. B.
2
2001
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
Easy and natural generation of multifractals: Multiplying harmonics of periodic functions. Zbl 0965.28003
Coppens, Marc-Olivier; Mandelbrot, Benoît B.
1
1999
Some mathematical questions arising in fractal geometry. Zbl 0963.37039
Mandelbrot, Benoît B.
1
2000
Variables et processus stochastiques de Pareto-Lévy, et la répartition des revenus. Zbl 0092.37504
Mandelbrot, Benoît
1
1959
Self-inverse fractals osculated by sigma-discs and the limit sets of inversion groups. Zbl 0609.30045
Mandelbrot, Benoit B.
1
1983
Self-similarity and covered neighborhoods of fractals: A random walk test. Zbl 0808.60037
Stauffer, D.; Aharony, A.; Mandelbrot, B. B.
1
1993
Géométrie fractale de la turbulence. Dimension de Hausdorff, dispersion et nature des singularites du mouvement des fluides. Zbl 0372.76044
Mandelbrot, Benoit
1
1976
Parallel cartoons of fractal models of finance. Zbl 1233.91344
Mandelbrot, Benoit B.
1
2005
The fractalist. Memoir of a scientific maverick. With an afterword by Michael Frame. Zbl 1270.01017
Mandelbrot, Benoît B.
1
2012
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 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
Scaling in financial prices. II: Multifractals and the star equation. Zbl 1405.91752
Mandelbrot, B. B.
1
2001
Scaling in financial prices. IV: Multifractal concentration. Zbl 1405.91754
Mandelbrot, B. B.
1
2001
The fractalist. Memoir of a scientific maverick. With an afterword by Michael Frame. Zbl 1270.01017
Mandelbrot, Benoît B.
1
2012
Convergence of complex multiplicative cascades. Zbl 1221.60028
Barral, Julien; Jin, Xiong; Mandelbrot, Benoît
18
2010
Uniform convergence for complex [0,1]-martingales. Zbl 1208.60035
Barral, Julien; Jin, Xiong; Mandelbrot, Benoît
10
2010
Fractional multiplicative processes. Zbl 1201.60035
Barral, Julien; Mandelbrot, Benoît
7
2009
A primer of negative test dimensions and degrees of emptiness for latent sets. Zbl 1168.28005
Mandelbrot, Benoit B.; Frame, Michael
2
2009
The inescapable need for fractal tools in finance. Zbl 1233.91345
Mandelbrot, Benoit B.
2
2005
Parallel cartoons of fractal models of finance. Zbl 1233.91344
Mandelbrot, Benoit B.
1
2005
The (mis)behavior of markets. A fractal view of risk, ruin and reward. Zbl 1140.91004
Mandelbrot, Benoit B.; Hudson, Richard L.
31
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.
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 1076.01037
Mandelbrot, Benoit B.
14
2004
Random multiplicative multifractal measures. I: Introduction to infinite products of independent random functions. Zbl 1088.28004
Barral, Julien; Mandelbrot, Benoît B.
12
2004
Multiperiodic multifractal martingale measures. Zbl 1047.28003
Barral, J.; Coppens, M.-O.; Mandelbrot, B. B.
8
2003
Multifractal power law distributions: Negative and critical dimensions and other “anomalies”, explained by a simple example. Zbl 1026.28007
Mandelbrot, Benoit B.
8
2003
Multifractal products of cylindrical pulses. Zbl 1014.60042
Barral, Julien; Mandelbrot, Benoît B.
70
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.
33
2002
Fractals, graphics, and mathematics education. Foreword by Lynn Arthur Steen. Zbl 1007.00010
3
2002
Topics on fractals in mathematics and physics. Zbl 0997.28004
Mandelbrot, Benoit B.
2
2001
Scaling in financial prices. I: Tails and dependence. Zbl 1405.91751
Mandelbrot, B. 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. II: Multifractals and the star equation. Zbl 1405.91752
Mandelbrot, B. B.
1
2001
Scaling in financial prices. IV: Multifractal concentration. Zbl 1405.91754
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.
38
1999
The canopy and shortest path in a self-contacting fractal tree. Zbl 1052.28500
Mandelbrot, Benoit B.; Frame, Michael
9
1999
Easy and natural generation of multifractals: Multiplying harmonics of periodic functions. Zbl 0965.28003
Coppens, Marc-Olivier; Mandelbrot, Benoît B.
1
1999
Exceptions to the multifractal formalism for discontinuous measures. Zbl 0892.28008
Riedi, Rudolph H.; Mandelbrot, Benoît B.
11
1998
Fractals and scaling in finance. Discontinuity, concentration, risk. Zbl 1005.91001
Mandelbrot, Benoit B.
175
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.
24
1996
Local regularity of nonsmooth wavelet expansions and application to the Polya function. Zbl 0916.42024
Jaffard, Stéphane; Mandelbrot, Benoît B.
15
1996
Exactly self-similar left-sided multifractals. 2nd rev. and enlarged ed. 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.
36
1995
Multifractal formalism for infinite multinomial measures. Zbl 0866.28005
Riedi, 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 0933.01025
Dauben, Joseph Warren
13
1995
Measures of fractal lacunarity: Minkowski content and alternatives. Zbl 0841.28010
Mandelbrot, Benoît B.
11
1995
Stable fractal sums of pulses: The cylindrical case. Zbl 0844.60017
Cioczek-Georges, Renata; Mandelbrot, Benoît B.; Samorodnitsky, Gennady; Taqqu, Murad S.
5
1995
Introduction to fractal sums of pulses. Zbl 0829.60032
Mandelbrot, Benoît B.
3
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
9
1994
Horton-Strahler ordering of random binary trees. Zbl 0820.60025
Yekutieli, Iddo; Mandelbrot, Benoit B.
5
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
2
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.
51
1991
Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism. Zbl 0850.76277
Mandelbrot, Benoît B.
11
1991
Negative fractal dimensions and multifractals. Zbl 0713.58034
Mandelbrot, Benoit B.
23
1990
Fractal geometry: What is it, and what does it do! Zbl 0746.00012
Mandelbrot, B. B.
24
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
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 0652.28002
Mandelbrot, Benoît B.
6
1987
The beauty of fractals. Images of complex dynamical systems. Zbl 0601.58003
Peitgen, H.-O.; Richter, P. H.
131
1986
Self-affine fractals and fractal dimension. Zbl 1063.28500
Mandelbrot, Benoit B.
28
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
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
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
5
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.
120
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.
1982
Fractal aspects of the iteration of \(z \to \lambda z(1-z)\) for complex \(\lambda\) and z. Zbl 0478.58017
Mandelbrot, Benoit B.
22
1980
Robust R/S analysis of long-run serial correlation. Zbl 0518.62036
Mandelbrot, Benoit B.; Taqqu, Murad S.
32
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.
241
1977
Fractals and turbulence: Attractors and dispersion. Zbl 0359.76050
Mandelbrot, Benoit B.
5
1977
Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3 + B. Zbl 0372.76043
Mandelbrot, Benoit
11
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.
47
1975
Limit theorems on the self normalized range for weakly and strongly dependent processes. Zbl 0288.60033
Mandelbrot, Benoit B.
33
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.
23
1975
Fonctions aléatoires pluri-temporelles: approximation poissonienne du cas brownien et généralisations. Zbl 0341.60008
Mandelbrot, Benoit
7
1975
Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. Zbl 0289.76031
Mandelbrot, Benoit B.
228
1974
Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire. Zbl 0276.60096
Mandelbrot, Benoit
41
1974
Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire: quelques extensions. Zbl 0276.60097
Mandelbrot, Benoit
20
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
12
1974
Comments on: ’A subordinated stochastic process model with finite variance for speculative prices’, by Peter K. Clark. Zbl 0308.90012
Mandelbrot, Benoit B.
4
1973
Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence. Zbl 0227.76081
Mandelbrot, Benoit B.
46
1972
Renewal sets and random cutouts. Zbl 0234.60102
Mandelbrot, Benoit B.
30
1972
On Dvoretzky coverings for the circle. Zbl 0222.60044
Mandelbrot, Benoit B.
13
1972
Long-run linearity, locally Gaussian process, H-spectra and infinite variances. Zbl 0191.51002
Mandelbrot, B.
27
1969
Fractional Brownian motions, fractional noises and applications. Zbl 0179.47801
Mandelbrot, B. B.; Van Ness, J. W.
1968
Some noises with \(1/f\) spectrum, a bridge between direct current and white noise. Zbl 0148.40507
Mandelbrot, Benoit
55
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.
10
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.
14
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
8
1962
Stable paretian random functions and the multiplicative variation of income. Zbl 0104.38402
Mandelbrot, Benoit
8
1961
Structure of language and its mathematical aspects. Zbl 0111.16102
3
1961
The Pareto-Lévy law and the distribution of income. Zbl 0201.51101
Mandelbrot, B.
67
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
6
1959
Variables et processus stochastiques de Pareto-Lévy, et la répartition des revenus. Zbl 0092.37504
Mandelbrot, Benoît
1
1959
Simple games of strategy occurring in communication through natural languages. Zbl 0059.13802
Mandelbrot, Benoit
2
1954
Contribution à la théorie mathématique des jeux de communication. Zbl 0053.40601
Mandelbrot, Benoit
4
1953
all top 5

Cited by 4,938 Authors

33 Jumarie, Guy M.
30 Barral, Julien
24 Anh, Vo V.
24 Taqqu, Murad S.
23 Mandelbrot, Benoit B.
17 Luo, Shaokai
16 Li, Ming
16 Seuret, Stéphane
15 Eliazar, Iddo I.
14 Chen, Yangquan
14 Nualart, David
14 Vargas, Vincent
13 Abry, Patrice
13 Jaffard, Stéphane
12 Băleanu, Dumitru I.
12 Deng, Weihua
12 Falconer, Kenneth J.
12 Leonenko, Nikolai N.
12 Rhodes, Rémi
12 Ruiz-Medina, María Dolores
11 Angulo, José Miguel
11 Muzy, Jean-François
11 Wang, Xingyuan
11 Wyłomańska, Agnieszka
10 Bacry, Emmanuel
10 Ben Slimane, Mourad
10 Cattani, Carlo
10 Chand, Arya Kumar Bedabrata
10 Chen, Yanguang
10 Jin, Xiong
10 Navascués, María Antonia
10 West, Bruce J.
9 Fernández Martínez, Manuel
9 Grigolini, Paolo
9 Lapidus, Michel L.
9 Liu, Shutang
9 Ostrovskii, Dmitrii M.
9 Romera, Miguel
9 Shang, Pengjian
9 Wang, Jun
9 Werner, Wendelin
9 Xu, Yanli
8 Coeurjolly, Jean-François
8 Hu, Yaozhong
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 Warma, Mahamadi
8 Wendt, Herwig
8 Xu, Yong
8 Zhao, Wei
7 Ahmed, Hamdy M.
7 Arneodo, Alain
7 Balankin, Alexander S.
7 Cohen, Serge
7 Didier, Gustavo
7 Duplantier, Bertrand
7 Feng, De-Jun
7 He, Jinman
7 Huang, Zhiyuan
7 Lacaux, Céline
7 Lévy Véhel, Jacques
7 Liu, Quansheng
7 Maslov, Viktor Pavlovich
7 Maslowski, Bohdan
7 McKibben, Mark Anthony
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 Chechkin, Aleksei V.
6 Duc, Luu Hoang
6 Fyodorov, Yan V.
6 Huillet, Thierry E.
6 Kurths, Jürgen
6 Lakhel, El Hassan
6 Lawler, Gregory Francis
6 Mehrdoust, Farshid
6 Meneveau, Charles
6 Nordman, Daniel J.
6 Sabzikar, Farzad
6 Telesca, Luciano
6 Unser, Michael A.
...and 4,838 more Authors
all top 5

Cited in 556 Serials

245 Chaos, Solitons and Fractals
176 Physica A
109 Fractals
101 Journal of Statistical Physics
85 Physica D
71 Stochastic Processes and their Applications
57 Physics Letters. A
54 Statistics & Probability Letters
49 Chaos
40 Applied Mathematics and Computation
38 Communications in Nonlinear Science and Numerical Simulation
36 Communications in Mathematical Physics
35 Stochastic Analysis and Applications
33 Journal of Mathematical Analysis and Applications
33 Journal of Econometrics
32 Journal of Fluid Mechanics
32 Journal of Theoretical Probability
29 Mathematical Problems in Engineering
27 Journal of Mathematical Physics
27 The Annals of Probability
27 Mathematical and Computer Modelling
26 Quantitative Finance
25 Probability Theory and Related Fields
24 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
23 Computers & Mathematics with Applications
23 Nonlinear Dynamics
22 Advances in Mathematics
22 Communications in Statistics. Theory and Methods
22 Bernoulli
22 Stochastics and Dynamics
21 The Annals of Applied Probability
20 Computational Statistics and Data Analysis
19 International Journal of Theoretical Physics
19 Discrete Dynamics in Nature and Society
18 Advances in Applied Probability
18 Journal of Computational and Applied Mathematics
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 Fractional Calculus & Applied Analysis
17 Advances in Difference Equations
16 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 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
13 Journal of Physics A: Mathematical and Theoretical
12 Applied Mathematics Letters
12 Physics of Fluids
12 Stochastics
11 Mathematics and Computers in Simulation
11 Theoretical Computer Science
11 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
11 Applied and Computational Harmonic Analysis
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 Economics Letters
10 Communications in Statistics. Simulation and Computation
10 Pattern Recognition
10 The Journal of Fourier Analysis and Applications
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 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 Journal of Mathematical Sciences (New York)
7 International Journal of Modern Physics C
7 Discrete and Continuous Dynamical Systems. Series B
7 Journal of Applied Mathematics and Computing
...and 456 more Serials
all top 5

Cited in 59 Fields

1,206 Probability theory and stochastic processes (60-XX)
654 Measure and integration (28-XX)
543 Statistics (62-XX)
441 Dynamical systems and ergodic theory (37-XX)
367 Statistical mechanics, structure of matter (82-XX)
349 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
230 Numerical analysis (65-XX)
228 Partial differential equations (35-XX)
219 Fluid mechanics (76-XX)
210 Real functions (26-XX)
183 Biology and other natural sciences (92-XX)
169 Computer science (68-XX)
138 Ordinary differential equations (34-XX)
123 Information and communication theory, circuits (94-XX)
107 Quantum theory (81-XX)
96 Systems theory; control (93-XX)
94 Harmonic analysis on Euclidean spaces (42-XX)
74 Mechanics of deformable solids (74-XX)
68 Number theory (11-XX)
67 Geophysics (86-XX)
65 Functions of a complex variable (30-XX)
54 Combinatorics (05-XX)
49 Operator theory (47-XX)
47 Operations research, mathematical programming (90-XX)
43 Relativity and gravitational theory (83-XX)
39 General topology (54-XX)
35 Classical thermodynamics, heat transfer (80-XX)
34 General and overarching topics; collections (00-XX)
34 Mechanics of particles and systems (70-XX)
32 Functional analysis (46-XX)
30 Global analysis, analysis on manifolds (58-XX)
29 Difference and functional equations (39-XX)
29 Approximations and expansions (41-XX)
27 Special functions (33-XX)
27 Calculus of variations and optimal control; optimization (49-XX)
24 Integral equations (45-XX)
23 Convex and discrete geometry (52-XX)
20 History and biography (01-XX)
20 Differential geometry (53-XX)
19 Integral transforms, operational calculus (44-XX)
16 Optics, electromagnetic theory (78-XX)
15 Mathematical logic and foundations (03-XX)
14 Astronomy and astrophysics (85-XX)
12 Group theory and generalizations (20-XX)
9 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

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