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Mandelbrot, Benoit B.

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Author ID: mandelbrot.benoit-b Recent zbMATH articles by "Mandelbrot, Benoit B."
Published as: Mandelbrot, B.; Mandelbrot, B. B.; Mandelbrot, Benoit; Mandelbrot, Benoit B.; Mandelbrot, Benoît; Mandelbrot, Benoît B.
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Documents Indexed: 122 Publications since 1951, including 18 Books
Biographic References: 49 Publications
all top 5

Serials

11 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris
5 Journal of Physics A: Mathematical and General
5 Quantitative Finance
5 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A
4 The Mathematical Intelligencer
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 Annals of Mathematical Statistics
1 Transactions of the IRE Professional Group on Information Theory

Publications by Year

Citations contained in zbMATH Open

91 Publications have been cited 4,117 times in 3,221 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.
935
1968
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.
274
1983
Fractals. Form, chance, and dimension. Translation. Zbl 0376.28020
Mandelbrot, Benoit B.
233
1977
Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. Zbl 0289.76031
Mandelbrot, Benoit B.
212
1974
Fractals and scaling in finance. Discontinuity, concentration, risk. Zbl 1005.91001
Mandelbrot, Benoit B.
165
1997
The fractal geometry of nature. Sonderausgabe. Zbl 0925.28001
Mandelbrot, Benoît B.
125
1991
Multifractal products of cylindrical pulses. Zbl 1014.60042
Barral, Julien; Mandelbrot, Benoît B.
66
2002
The Pareto-Lévy law and the distribution of income. Zbl 0201.51101
Mandelbrot, B.
58
1960
Fractals. Form, chance and dimension. Zbl 0900.00018
Mandelbrot, Benoît B.
46
1975
Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence. Zbl 0227.76081
Mandelbrot, Benoit B.
46
1972
Some noises with \(1/f\) spectrum, a bridge between direct current and white noise. Zbl 0148.40507
Mandelbrot, B.
46
1967
Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire. Zbl 0276.60096
Mandelbrot, Benoit
40
1974
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
38
1988
A class of micropulses and antipersistent fractional Brownian motion. Zbl 0846.60055
Cioczek-Georges, Renata; Mandelbrot, Benoît B.
35
1995
Multifractals and 1/f noise. Wild self-affinity in physics (1963–1976). Selecta volume. Zbl 0956.28005
Mandelbrot, Benoît B.
34
1999
The (mis)behavior of markets. A fractal view of risk, ruin and reward. Zbl 1140.91004
Mandelbrot, Benoit B.; Hudson, Richard L.
33
2004
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.
31
2002
Robust R/S analysis of long-run serial correlation. Zbl 0518.62036
Mandelbrot, Benoit B.; Taqqu, Murad S.
31
1979
Limit theorems on the self normalized range for weakly and strongly dependent processes. Zbl 0288.60033
Mandelbrot, Benoit B.
30
1975
Renewal sets and random cutouts. Zbl 0234.60102
Mandelbrot, Benoit B.
30
1972
Long-run linearity, locally Gaussian process, H-spectra and infinite variances. Zbl 0191.51002
Mandelbrot, B.
26
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
Fractal aspects of the iteration of \(z \to \lambda z(1-z)\) for complex \(\lambda\) and z. Zbl 0478.58017
Mandelbrot, Benoit B.
24
1980
Negative fractal dimensions and multifractals. Zbl 0713.58034
Mandelbrot, Benoit B.
23
1990
Self-affine fractals and fractal dimension. Zbl 1063.28500
Mandelbrot, Benoit B.
22
1985
On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars. Zbl 0329.76047
Mandelbrot, Benoit B.
21
1975
Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire: quelques extensions. Zbl 0276.60097
Mandelbrot, Benoit
18
1974
Convergence of complex multiplicative cascades. Zbl 1221.60028
Barral, Julien; Jin, Xiong; Mandelbrot, Benoît
17
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.
15
2004
Multifractal formalism for infinite multinomial measures. Zbl 0866.28005
Riedi, Rudolf H.; Mandelbrot, Benoît B.
15
1995
The role of sufficiency and of estimation in thermodynamics. Zbl 0111.33705
Mandelbrot, B.
15
1962
Local regularity of nonsmooth wavelet expansions and application to the Polya function. Zbl 0916.42024
Jaffard, Stéphane; Mandelbrot, Benoît B.
14
1996
Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3 + B. Zbl 0372.76043
Mandelbrot, Benoit
13
1976
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.
11
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.
11
2004
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
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
11
1974
Les objects fractals. Forme, hasard et dimension. (Fractals. Forme, chance and dimension). 2ème éd. 2ème éd. Zbl 0995.00503
Mandelbrot, Benoit
10
1984
Une classe de processus stochastiques homothetiques à soi; application à la loi climatologique de H.E. Hurst. Zbl 0127.09501
Mandelbrot, B.
10
1965
Uniform convergence for complex [0,1]-martingales. Zbl 1208.60035
Barral, Julien; Jin, Xiong; Mandelbrot, Benoît
9
2010
The canopy and shortest path in a self-contacting fractal tree. Zbl 1052.28500
Mandelbrot, Benoit B.; Frame, Michael
9
1999
Measures of fractal lacunarity: Minkowski content and alternatives. Zbl 0841.28010
Mandelbrot, Benoît B.
9
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
Multifractal power law distributions: Negative and critical dimensions and other “anomalies”, explained by a simple example. Zbl 1026.28007
Mandelbrot, Benoit B.
8
2003
Inversion formula for continuous multifractals. Zbl 0892.28007
Riedi, Rudolf H.; Mandelbrot, Benoît B.
8
1997
Fractals and turbulence: Attractors and dispersion. Zbl 0359.76050
Mandelbrot, Benoit B.
8
1977
Fractional multiplicative processes. Zbl 1201.60035
Barral, Julien; Mandelbrot, Benoît
7
2009
Multiperiodic multifractal martingale measures. Zbl 1047.28003
Barral, J.; Coppens, M.-O.; Mandelbrot, B. B.
7
2003
Inverse measures, the inversion formula, and discontinuous multifractals. Zbl 0870.28004
Mandelbrot, Benoît B.; Riedi, Rudolf H.
7
1997
Fonctions aléatoires pluri-temporelles: approximation poissonienne du cas brownien et généralisations. Zbl 0341.60008
Mandelbrot, Benoit
7
1975
Sur certains prix spéculatifs: faits empiriques et modèle basé sur les processus stables additifs non gaussiens de Paul Lévy. Zbl 0100.34904
Mandelbrot, Benoit
6
1962
Stable paretian random functions and the multiplicative variation of income. Zbl 0104.38402
Mandelbrot, Benoit
6
1961
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
Exactly self-similar left-sided multifractals. Zbl 0850.28004
Mandelbrot, Benoît B.; Evertsz, Carl J. G.
5
1996
Stable fractal sums of pulses: The cylindrical case. Zbl 0844.60017
Cioczek-Georges, Renata; Mandelbrot, Benoît B.; Samorodnitsky, Gennady; Taqqu, Murad S.
5
1995
Ensembles de multiplicité aléatoires. Zbl 0135.27106
Kahane, J. P.; Mandelbrot, B.
5
1965
Contribution à la théorie mathématique des jeux de communication. Zbl 0053.40601
Mandelbrot, Benoit
5
1953
Peano-Pólya motions, when time is intrinsic or binomial (uniform or multifractal). Zbl 0922.28006
Mandelbrot, Benoît B.; Jaffard, Stéphane
4
1997
Horton-Strahler ordering of random binary trees. Zbl 0820.60025
Yekutieli, Iddo; Mandelbrot, Benoit B.
4
1994
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.
4
1987
On fractal geometry, and a few of the mathematical questions it has raised. Zbl 0562.01012
Mandelbrot, Benoit B.
4
1984
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
Fractals, graphics, and mathematics education. Foreword by Lynn Arthur Steen. Zbl 1007.00010
Frame, Michael (ed.); Mandelbrot, Benoit B. (ed.)
3
2002
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
Introduction to fractal sums of pulses. Zbl 0829.60032
Mandelbrot, Benoît B.
3
1995
New methods in statistical economics. Zbl 0121.15105
Mandelbrot, B.
3
1964
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
Topics on fractals in mathematics and physics. Zbl 0997.28004
Mandelbrot, Benoit B.
2
2001
Antipodal correlations and the texture (fractal lacunarity) in critical percolation clusters. Zbl 0843.58112
Mandelbrot, Benoît B.; Stauffer, Dietrich
2
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
Directed recursive models for fractal growth. Zbl 0703.58034
Mandelbrot, Benoit B.; Vicsek, Tamás
2
1989
Self-inverse fractals osculated by sigma-discs and the limit sets of inversion groups. Zbl 0609.30045
Mandelbrot, Benoit B.
2
1983
Colliers aléatoires et une alternative aux promenades au hasard sans boucle: les cordonnets discrets et fractals. Zbl 0386.60049
Mandelbrot, Benoit
2
1978
Simple games of strategy occurring in communication through natural languages. Zbl 0059.13802
Mandelbrot, Benoit
2
1954
The fractalist. Memoir of a scientific maverick. With an afterword by Michael Frame. Zbl 1270.01017
Mandelbrot, Benoît B.
1
2012
Parallel cartoons of fractal models of finance. Zbl 1233.91344
Mandelbrot, Benoit B.
1
2005
Scaling in financial prices. I: Tails and dependence. Zbl 1405.91751
Mandelbrot, B. B.
1
2001
Some mathematical questions arising in fractal geometry. Zbl 0963.37039
Mandelbrot, Benoît B.
1
2000
Easy and natural generation of multifractals: Multiplying harmonics of periodic functions. Zbl 0965.28003
Coppens, Marc-Olivier; Mandelbrot, Benoît B.
1
1999
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. 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. 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 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
Géométrie fractale de la turbulence. Dimension de Hausdorff, dispersion et nature des singularites du mouvement des fluides. Zbl 0372.76044
Mandelbrot, Benoit
1
1976
Sporadic random functions and conditional spectral analysis: Self-similar examples and limits. Zbl 0189.18302
Mandelbrot, B.
1
1967
Variables et processus stochastiques de Pareto-Lévy, et la répartition des revenus. Zbl 0092.37504
Mandelbrot, Benoît
1
1959
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
17
2010
Uniform convergence for complex [0,1]-martingales. Zbl 1208.60035
Barral, Julien; Jin, Xiong; Mandelbrot, Benoît
9
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.
33
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.
15
2004
Random multiplicative multifractal measures. I: Introduction to infinite products of independent random functions. Zbl 1088.28004
Barral, Julien; Mandelbrot, Benoît B.
11
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.
11
2004
Multifractal power law distributions: Negative and critical dimensions and other “anomalies”, explained by a simple example. Zbl 1026.28007
Mandelbrot, Benoit B.
8
2003
Multiperiodic multifractal martingale measures. Zbl 1047.28003
Barral, J.; Coppens, M.-O.; Mandelbrot, B. B.
7
2003
Multifractal products of cylindrical pulses. Zbl 1014.60042
Barral, Julien; Mandelbrot, Benoît B.
66
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.
31
2002
Fractals, graphics, and mathematics education. Foreword by Lynn Arthur Steen. Zbl 1007.00010
Frame, Michael (ed.); Mandelbrot, Benoit B. (ed.)
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.
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.
34
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.
165
1997
Inversion formula for continuous multifractals. Zbl 0892.28007
Riedi, Rudolf H.; Mandelbrot, Benoît B.
8
1997
Inverse measures, the inversion formula, and discontinuous multifractals. Zbl 0870.28004
Mandelbrot, Benoît B.; Riedi, Rudolf H.
7
1997
Peano-Pólya motions, when time is intrinsic or binomial (uniform or multifractal). Zbl 0922.28006
Mandelbrot, Benoît B.; Jaffard, Stéphane
4
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.
14
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.
35
1995
Multifractal formalism for infinite multinomial measures. Zbl 0866.28005
Riedi, Rudolf H.; Mandelbrot, Benoît B.
15
1995
Measures of fractal lacunarity: Minkowski content and alternatives. Zbl 0841.28010
Mandelbrot, Benoît B.
9
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
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
Introduction to fractal sums of pulses. Zbl 0829.60032
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.
4
1994
Antipodal correlations and the texture (fractal lacunarity) in critical percolation clusters. Zbl 0843.58112
Mandelbrot, Benoît B.; Stauffer, Dietrich
2
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
The fractal geometry of nature. Sonderausgabe. Zbl 0925.28001
Mandelbrot, Benoît B.
125
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
38
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.
4
1987
Self-affine fractals and fractal dimension. Zbl 1063.28500
Mandelbrot, Benoit B.
22
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. 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. 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
Les objects fractals. Forme, hasard et dimension. (Fractals. Forme, chance and dimension). 2ème éd. 2ème éd. Zbl 0995.00503
Mandelbrot, Benoit
10
1984
On fractal geometry, and a few of the mathematical questions it has raised. Zbl 0562.01012
Mandelbrot, Benoit B.
4
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.
274
1983
Self-inverse fractals osculated by sigma-discs and the limit sets of inversion groups. Zbl 0609.30045
Mandelbrot, Benoit B.
2
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.
24
1980
Robust R/S analysis of long-run serial correlation. Zbl 0518.62036
Mandelbrot, Benoit B.; Taqqu, Murad S.
31
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.
233
1977
Fractals and turbulence: Attractors and dispersion. Zbl 0359.76050
Mandelbrot, Benoit B.
8
1977
Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3 + B. Zbl 0372.76043
Mandelbrot, Benoit
13
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. Zbl 0900.00018
Mandelbrot, Benoît B.
46
1975
Limit theorems on the self normalized range for weakly and strongly dependent processes. Zbl 0288.60033
Mandelbrot, Benoit B.
30
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.
21
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.
212
1974
Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire. Zbl 0276.60096
Mandelbrot, Benoit
40
1974
Multiplications aléatoires iterées et distributions invariantes par moyenne ponderee aléatoire: quelques extensions. Zbl 0276.60097
Mandelbrot, Benoit
18
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
11
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.
26
1969
Fractional Brownian motions, fractional noises and applications. Zbl 0179.47801
Mandelbrot, B. B.; Van Ness, J. W.
935
1968
Some noises with \(1/f\) spectrum, a bridge between direct current and white noise. Zbl 0148.40507
Mandelbrot, B.
46
1967
Sporadic random functions and conditional spectral analysis: Self-similar examples and limits. Zbl 0189.18302
Mandelbrot, B.
1
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.
15
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
6
1962
Stable paretian random functions and the multiplicative variation of income. Zbl 0104.38402
Mandelbrot, Benoit
6
1961
The Pareto-Lévy law and the distribution of income. Zbl 0201.51101
Mandelbrot, B.
58
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
5
1953
all top 5

Cited by 4,792 Authors

34 Jumarie, Guy M.
30 Barral, Julien
23 Mandelbrot, Benoit B.
23 Taqqu, Murad S.
22 Anh, Vo V.
17 Luo, Shaokai
16 Chen, Yangquan
15 Li, Ming
15 Wang, Xingyuan
14 Nualart, David
14 Seuret, Stéphane
14 Vargas, Vincent
13 Eliazar, Iddo I.
12 Abry, Patrice
12 Deng, Weihua
12 Leonenko, Nikolai N.
12 Rhodes, Rémi
12 Ruiz-Medina, María Dolores
11 Angulo, José Miguel
11 Băleanu, Dumitru I.
11 Falconer, Kenneth J.
11 Jaffard, Stéphane
10 Bacry, Emmanuel
10 Jin, Xiong
10 Muzy, Jean-François
9 Ben Slimane, Mourad
9 Cattani, Carlo
9 Chen, Yanguang
9 Ostrovskii, Dmitrii M.
9 Panagiotopoulos, Panagiotis D.
9 Romera, Miguel
9 Wang, Jun
9 Werner, Wendelin
9 West, Bruce J.
9 Xu, Yanli
8 Chand, Arya Kumar Bedabrata
8 Fernández Martínez, Manuel
8 Grigolini, Paolo
8 Hu, Yaozhong
8 Lapidus, Michel L.
8 Lévy Véhel, Jacques
8 Meerschaert, Mark M.
8 Montoya, Fausto
8 Navascués, María Antonia
8 Nottale, Laurent
8 Ostoja-Starzewski, Martin
8 Panagouli, O. K.
8 Pastor, Gerardo
8 Rachev, Svetlozar T.
8 Shang, Pengjian
8 Xu, Yong
8 Zhao, Wei
7 Arneodo, Alain
7 Balankin, Alexander S.
7 Barnsley, Michael Fielding
7 Coeurjolly, Jean-François
7 Cohen, Serge
7 Duplantier, Bertrand
7 Feng, De-Jun
7 He, Jinman
7 Huang, Zhiyuan
7 Lacaux, Céline
7 Lai, Dejian
7 Maslov, Viktor Pavlovich
7 Øksendal, Bernt Karsten
7 Ouknine, Youssef
7 Pei, Bin
7 Peyrière, Jacques
7 Saksman, Eero
7 Sornette, Didier
7 Telesca, Luciano
7 Warma, Mahamadi
7 Wendt, Herwig
7 Yu, Boming
7 Yu, Zuguo
7 Zhang, Xiaotian
6 Agop, Maricel
6 Beran, Jan
6 Biermé, Hermine
6 Carpinteri, Alberto
6 Chechkin, Aleksei V.
6 Didier, Gustavo
6 Fyodorov, Yan V.
6 Huillet, Thierry E.
6 Lawler, Gregory Francis
6 Liu, Quansheng
6 Liu, Shutang
6 Maslowski, Bohdan
6 McKibben, Mark Anthony
6 Meneveau, Charles
6 Mistakidis, E. S.
6 Nordman, Daniel J.
6 Pietronero, Luciano
6 Sánchez Granero, Miguel Ángel
6 Suomala, Ville
6 Unser, Michael A.
6 Webb, Christian
6 Wyłomańska, Agnieszka
6 Xu, Mingyu
6 Yan, Litan
...and 4,692 more Authors
all top 5

Cited in 531 Serials

246 Chaos, Solitons and Fractals
124 Physica A
100 Journal of Statistical Physics
93 Physica D
81 Fractals
70 Stochastic Processes and their Applications
62 Physics Letters. A
49 Statistics & Probability Letters
48 Applied Mathematics and Computation
45 Chaos
36 Communications in Mathematical Physics
35 Mathematical and Computer Modelling
35 Communications in Nonlinear Science and Numerical Simulation
34 Journal of Mathematical Analysis and Applications
33 Journal of Econometrics
32 Stochastic Analysis and Applications
29 Mathematical Problems in Engineering
28 Journal of Theoretical Probability
27 Journal of Fluid Mechanics
27 The Annals of Probability
25 Computers & Mathematics with Applications
25 Journal of Mathematical Physics
25 Probability Theory and Related Fields
23 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
23 Quantitative Finance
22 Nonlinear Dynamics
21 Advances in Mathematics
21 Bernoulli
20 Journal of Statistical Planning and Inference
20 Computational Statistics and Data Analysis
19 International Journal of Theoretical Physics
19 Journal of Computational and Applied Mathematics
19 The Annals of Applied Probability
19 Stochastics and Dynamics
18 Communications in Statistics. Theory and Methods
17 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
17 Journal of Time Series Analysis
16 Journal of the Franklin Institute
16 Transactions of the American Mathematical Society
16 Discrete Dynamics in Nature and Society
15 Advances in Applied Probability
15 Journal of Computational Physics
15 The Annals of Statistics
15 Applied Mathematical Modelling
15 Fractional Calculus & Applied Analysis
15 Journal of Statistical Mechanics: Theory and Experiment
15 Journal of Theoretical Biology
14 Mathematical Biosciences
14 The Mathematical Intelligencer
13 Physics Reports
13 Theoretical Computer Science
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 Acta Mechanica
12 Applied Mathematics Letters
12 Physics of Fluids
12 Advances in Difference Equations
12 The European Physical Journal B. Condensed Matter and Complex Systems
11 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
11 Applied and Computational Harmonic Analysis
11 Journal of Applied Statistics
11 Econometric Theory
10 Proceedings of the American Mathematical Society
10 Acta Applicandae Mathematicae
10 Economics Letters
10 Pattern Recognition
10 Statistical Inference for Stochastic Processes
10 Stochastics
9 International Journal of Heat and Mass Transfer
9 Israel Journal of Mathematics
9 Applied Numerical Mathematics
9 Japan Journal of Applied Mathematics
9 Constructive Approximation
9 Signal Processing
9 The Journal of Fourier Analysis and Applications
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 Annals of Physics
8 Communications in Statistics. Simulation and Computation
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 Multivariate Analysis
7 Mathematics and Computers in Simulation
7 Journal of Mathematical Sciences (New York)
7 International Journal of Modern Physics C
7 Discrete and Continuous Dynamical Systems. Series B
7 SIAM Journal on Financial Mathematics
6 Modern Physics Letters B
...and 431 more Serials
all top 5

Cited in 59 Fields

1,133 Probability theory and stochastic processes (60-XX)
625 Measure and integration (28-XX)
507 Statistics (62-XX)
444 Dynamical systems and ergodic theory (37-XX)
333 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
304 Statistical mechanics, structure of matter (82-XX)
214 Numerical analysis (65-XX)
211 Fluid mechanics (76-XX)
201 Partial differential equations (35-XX)
188 Biology and other natural sciences (92-XX)
187 Real functions (26-XX)
179 Computer science (68-XX)
122 Ordinary differential equations (34-XX)
113 Information and communication theory, circuits (94-XX)
109 Quantum theory (81-XX)
88 Harmonic analysis on Euclidean spaces (42-XX)
88 Systems theory; control (93-XX)
76 Mechanics of deformable solids (74-XX)
66 Number theory (11-XX)
64 Geophysics (86-XX)
60 Functions of a complex variable (30-XX)
50 Combinatorics (05-XX)
46 Operations research, mathematical programming (90-XX)
43 Relativity and gravitational theory (83-XX)
42 Operator theory (47-XX)
39 General topology (54-XX)
37 Mechanics of particles and systems (70-XX)
31 General and overarching topics; collections (00-XX)
29 Difference and functional equations (39-XX)
29 Approximations and expansions (41-XX)
28 Global analysis, analysis on manifolds (58-XX)
28 Classical thermodynamics, heat transfer (80-XX)
26 Functional analysis (46-XX)
25 Special functions (33-XX)
24 Calculus of variations and optimal control; optimization (49-XX)
24 Convex and discrete geometry (52-XX)
22 Integral equations (45-XX)
20 History and biography (01-XX)
17 Differential geometry (53-XX)
16 Mathematical logic and foundations (03-XX)
16 Integral transforms, operational calculus (44-XX)
16 Optics, electromagnetic theory (78-XX)
14 Astronomy and astrophysics (85-XX)
12 Group theory and generalizations (20-XX)
10 Linear and multilinear algebra; matrix theory (15-XX)
9 Manifolds and cell complexes (57-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 Sequences, series, summability (40-XX)
2 Algebraic geometry (14-XX)
2 Category theory; homological algebra (18-XX)
2 Several complex variables and analytic spaces (32-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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