Most cited papers in Mathematical Dynamics and Fractals
What are the most cited papers in Mathematical Dynamics and Fractals?
The most cited paper in Mathematical Dynamics and Fractals is "Measuring the strangeness of strange attractors" (Peter Grassberger, Itamar Procaccia, 1983), with 5,689 citations. Next come "Ergodic theory of chaos and strange attractors" (4,989) and "An equation for continuous chaos" (4,050).
Showing 50 of 100 papers. Every paper with more than 602 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Measuring the strangeness of strange attractors Peter Grassberger, Itamar Procaccia · Physica D Nonlinear Phenomena | Oct 1983 | 5,689 |
| 2 | Ergodic theory of chaos and strange attractors Jean‐Pierre Eckmann, David Pierre Ruelle · Reviews of Modern Physics | Jul 1985 | 4,989 |
| 3 | An equation for continuous chaos Otto E. Rössler · Physics Letters A | Jul 1976 | 4,050 |
| 4 | Differentiable Dynamical Systems Steve Smale | 1980 | 2,543 |
| 5 | An Introduction to Chaotic Dynamical Systems Robert L. Devaney, Jean‐Pierre Eckmann · Physics Today | Jul 1987 | 2,385 |
| 6 | Approach to an irregular time series on the basis of the fractal theory Tomoyuki Higuchi · Physica D Nonlinear Phenomena | Jun 1988 | 2,195 |
| 7 | Embedology TIMOTHY D. SAUER, James A. Yorke, Martin Casdagli · Journal of Statistical Physics | Nov 1991 | 2,046 |
| 8 | Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory Giancarlo Benettin, L. Galgani, Antonio Giorgilli et al. · Meccanica | Mar 1980 | 1,973 |
| 9 | Chaos in Dynamical Systems Daniel I. Zwillinger · Elsevier eBooks | 1992 | 1,964 |
| 10 | Universality and complexity in cellular automata Stephen Wolfram · Physica D Nonlinear Phenomena | 1984 | 1,944 |
| 11 | Symmetric Ciphers Based on Two-Dimensional Chaotic Maps Jiří Fridrich · International Journal of Bifurcation and Chaos | Jun 1998 | 1,918 |
| 12 | A NEW CHAOTIC ATTRACTOR COINED Jinhu Lü, Guanrong Chen · International Journal of Bifurcation and Chaos | Mar 2002 | 1,866 |
| 13 | Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits) Michael Gromov · Publications mathématiques de l IHÉS | 7 Dec 1981 | 1,846 |
| 14 | The infinite number of generalized dimensions of fractals and strange attractors H. G. E. Hentschel, Itamar Procaccia · Physica D Nonlinear Phenomena | Sep 1983 | 1,814 |
| 15 | Periodic Orbits and Classical Quantization Conditions Martin C. Gutzwiller · Journal of Mathematical Physics | Mar 1971 | 1,544 |
| 16 | Self-similarity and intermediate asymptotics Grigory Isaakovich Barenblatt · Cambridge University Press eBooks | 13 Nov 2003 | 1,494 |
| 17 | Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits Eric J. Heller · Physical Review Letters | 15 Oct 1984 | 1,485 |
| 18 | Chaos: An Introduction to Dynamical Systems Kathleen T. Alligood, TIMOTHY D. SAUER, James A. Yorke et al. · Physics Today | Nov 1997 | 1,469 |
| 19 | Nonlocal Operators with Applications to Image Processing Guy Gilboa, Stanley Osher · Multiscale Modeling and Simulation | 12 Nov 2008 | 1,439 |
| 20 | Convergence of Probability Measures James L. Snell · Technometrics | Feb 1970 | 1,379 |
| 21 | Crises, sudden changes in chaotic attractors, and transient chaos Celso Grebogi, Edward Ott, James A. Yorke · Physica D Nonlinear Phenomena | May 1983 | 1,332 |
| 22 | Introduction to Percolation Theory N. Rivier · Physics Bulletin | Nov 1987 | 1,305 |
| 23 | Image coding based on a fractal theory of iterated contractive image transformations Arnaud E. Jacquin · IEEE Transactions on Image Processing | 1992 | 1,274 |
| 24 | Image encryption using chaotic logistic map Narendra Kumar Pareek, Vinod Patidar, K. K. Sud · Image and Vision Computing | 18 Apr 2006 | 1,265 |
| 25 | Mathematical problems for the next century Steve Smale · The Mathematical Intelligencer | Mar 1998 | 1,261 |
| 26 | Flow by mean curvature of convex surfaces into spheres Gerhard Huisken · Journal of Differential Geometry | 1984 | 1,227 |
| 27 | Motion of level sets by mean curvature. I L. C. Evans, Joel Spruck · Journal of Differential Geometry | 1991 | 1,220 |
| 28 | Optical encryption by double-random phase encoding in the fractional Fourier domain G. Unnikrishnan, Joby Joseph, K. Singh · Optics Letters | 15 Jun 2000 | 1,190 |
| 29 | Scale Mixtures of Normal Distributions David F. Andrews, C. L. Mallows · Journal of the Royal Statistical Society Series B (Statistical Methodology) | Sep 1974 | 1,189 |
| 30 | Correlation inequalities on some partially ordered sets C.M. Fortuin, Piet Kasteleyn, J. Ginibre · Communications in Mathematical Physics | Jun 1971 | 1,157 |
| 31 | The dimension of chaotic attractors J. Doyne Farmer, Edward Ott, James A. Yorke · Physica D Nonlinear Phenomena | May 1983 | 1,115 |
| 32 | On a theory of computation and complexity over the real numbers: 𝑁𝑃- completeness, recursive functions and universal machines Lenore Blum, Mike Shub, Steve Smale · Bulletin of the American Mathematical Society | 1989 | 1,070 |
| 33 | Endomorphisms and automorphisms of the shift dynamical system Gustav A. Hedlund · Theory of Computing Systems | Dec 1969 | 1,065 |
| 34 | Semiclassical theory of spectral rigidity Michael Berry · Proceedings of the Royal Society of London A Mathematical and Physical Sciences | 8 Aug 1985 | 1,058 |
| 35 | A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems I. Shimada, Tomohiro Nagashima · Progress of Theoretical Physics | Jun 1979 | 1,050 |
| 36 | Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application Giancarlo Benettin, L. Galgani, Antonio Giorgilli et al. · Meccanica | Mar 1980 | 1,032 |
| 37 | Image rotation, Wigner rotation, and the fractional Fourier transform Adolf W. Lohmann · Journal of the Optical Society of America A | Oct 1993 | 1,022 |
| 38 | Self-Affine Fractals and Fractal Dimension Benoît B. Mandelbrot · Physica Scripta | Oct 1985 | 1,017 |
| 39 | Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation Harry Furstenberg · Theory of Computing Systems | Mar 1967 | 1,014 |
| 40 | Attractors for random dynamical systems Hans Crauel, Franco Flandoli · Probability Theory and Related Fields | Sep 1994 | 1,006 |
| 41 | Lyapunov exponents, entropy and periodic orbits for diffeomorphisms Anatole Katok · Publications mathématiques de l IHÉS | 7 Dec 1980 | 999 |
| 42 | On the concept of attractor John Milnor · Communications in Mathematical Physics | Jun 1985 | 993 |
| 43 | Random walks on fractal structures and percolation clusters R. Rammal, G. Toulouse · Journal de Physique Lettres | 1983 | 977 |
| 44 | Iterated function systems and the global construction of fractals Michael Fielding Barnsley, Stephen G. Demko · Proceedings of the Royal Society of London A Mathematical and Physical Sciences | 8 Jun 1985 | 975 |
| 45 | Estimating fractal dimension James P. Theiler · Journal of the Optical Society of America A | Jun 1990 | 967 |
| 46 | The control of chaos: theory and applications Stefano Boccaletti · Physics Reports | May 2000 | 953 |
| 47 | Fractal Image Compression: Theory and Application Yuval Fisher | 12 Oct 2011 | 953 |
| 48 | Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions Richard C. Bradley · Probability Surveys | 2005 | 922 |
| 49 | Fractal functions and interpolation Michael Fielding Barnsley · Constructive Approximation | Dec 1986 | 915 |
| 50 | Chaotic attractors of an infinite-dimensional dynamical system J. Doyne Farmer · Physica D Nonlinear Phenomena | Mar 1982 | 903 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.