Ergodic theory of chaos and strange attractors

Reviews of Modern Physics

Volumn 57, Issue 3, 1985, Pages 617-656

  Eckmann, J P ^a   Ruelle, D ^b  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 35949018382     PISSN: 00346861     EISSN: None     Source Type: Journal    
DOI: 10.1103/RevModPhys.57.617     Document Type: Article

References (147)

1. Testing nonlinear dynamics
2. Topological entropy
3. Fat baker's transformations
4. Geodesic flows on a compact Riemann manifold of negative curvature
5. On iterations of 1-ax2 on (-1,1)
6. Kolmogorov entropy and numerical experiments
7. Tous les nombres de Liapounov sont effectivement calculables
8. The ergodic theory of Axiom A flows
9. Partial regularity of suitable weak solutions of the Navier-Stokes equations
10. Two remarks on the computer study of differentiable dynamical systems
11. Order in Chaos: Proceedings of the International Conference... Los Alamos,... 1982
12. On computing the Kolmogorov entropy from the time signals of dissipative and conservative dynamical systems
13. Universal properties of maps of an interval
14. Positive Liapunov exponents and absolute continuity for maps of the interval
15. Déterminisme et chaos
16. On the Hénon transformation
17. On computing the entropy of the Hénon attractor
18. Dimension de Hausdorff des attracteurs
19. Experimental aspects of the transition to turbulence in Rayleigh-Bénard convection
20. Roads to turbulence in dissipative dynamical systems
21. A proof of Pesin's stable manifold theorem
22. Quantitative universality for a class of nonlinear transformations
23. The universal metric properties of nonlinear transformations
24. The transition to aperiodic behavior in turbulent systems
25. Characteristic exponents and strange attractors
26. Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
27. The Lyapunov dimension of strange attractors
28. Intermittency in nonlinear dynamics and singularities at complex times
29. On the Hausdorff dimension of fractal attractors
30. Noise in chaotic systems
31. Bifurcation Theory and Applications in Scientific Disciplines
32. International Conference on Nonlinear Dynamics
33. A two-dimensional mapping with a strange attractor
34. The applicability of the third integral of motion some numerical experiments
35. On the dimension of attractors of k-contracting systems in an infinite dimensional space
36. Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
37. Preturbulence: a regime observed in a fluid flow model of Lorenz
38. Liapunov exponents, entropy and periodic orbits for diffeomorphisms
39. On small random perturbations of some smooth dynamical systems
40. The metric entropy of diffeomorphisms
41. Period three implies chaos
42. Une expérience de Rayleigh-Bénard de géométrie réduite; multiplication, accrochage, et démultiplication de fréquences
43. On characteristic exponents in turbulence
44. Deterministic nonperiodic flow
45. The Physics of Chaos and Related Problems: Proceedings of the 59th Nobel Symposium, 1984
46. Negatively invariant sets of compact maps and an extension of a theorem of Cartwright
47. Dimension of strange attractors: an experimental determination for the chaotic regime of two convective systems
48. On the dimension of the compact invariant sets of certain nonlinear maps
49. Liapunov exponents and stable manifolds for compact transformations
50. The dimension of the maximal measure for a polynomial map
51. Hausdorff dimension orthogonal projections and intersections with planes
52. Hausdorff dimension for horseshoes
53. On the concept of attractor
54. Structure of mappings of an interval with zero entropy
55. Diffeomorphisms with infinitely many sinks
56. The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
57. Occurrence of strange axiom A attractors near quasiperiodic flows on Tm, m≥3
58. A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems
59. Invariant manifold families which correspond to nonvanishing characteristic exponents
60. Lyapunov characteristic exponents and smooth ergodic theory
61. The static and dynamic invariants that characterize chaos and the relations between them in theory and experiments
62. A proof of Oseledec's multiplicative ergodic theorem
63. Neutron scattering from a convecting nematic: multicriticality, multistability and chaos
64. An equation for continuous chaos
65. Observation of a strange attractor
66. Topology of chaos in a chemical reaction
67. A measure associated with Axiom A attractors
68. An inequality for the entropy of differentiable maps
69. Ergodic theory of differentiable dynamical systems
70. Measures describing a turbulent flow
71. Small random perturbations of dynamical systems and the definition of attractors
72. Characteristic Exponents and Invariant Manifolds in Hilbert Space
73. Characteristic exponents for a viscous fluid subjected to time dependent forces
74. On the nature of turbulence
75. Strange attractors, chaotic behavior and information flow
76. Gibbsian distribution on the Lorenz attractor
77. Gibbs measures in ergodic theory
78. Differentiable dynamical systems
79. Detecting strange attractors in turbulence
80. Invariants related to dimension and entropy
81. Discrete population models and chaos
82. Universality of Feigenbaum and thermodynamic formalism
83. Nonchaotic Rayleigh-Bénard convection with four and five incommensurate frequencies
84. Determining Liapunov exponents from a time series
85. Capacity of attractors
86. Dimension, entropy and Liapunov exponents
87. Dimension, entropy and Liapunov exponents in differentiable dynamical systems