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Ergodic theory of differentiable dynamical systems
Abstract
If f is a C 1 + ɛ diffeomorphism of a compact manifold M, we prove the existence of stable manifolds, almost everywhere with respect to every f -invariant probability measure on M. These stable manifolds are smooth but do not in general constitute a continuous family. The proof of this stable manifold theorem (and similar results) is through the study of random matrix products (multiplicative ergodic theorem) and perturbation of such products.
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Citations
Cited by
Ergodic theory of chaos and strange attractors
Eckmann, J. P., & Ruelle, D. (1985) · Reviews of Modern Physics · doi:10.1103/revmodphys.57.617 · Cited by 4,941
Self-citationLyapunov exponents, entropy and periodic orbits for diffeomorphisms
Katok, A. (1980) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02684777 · Cited by 935
Probability: Theory and Examples
Durrett, R. (2019) · doi:10.1017/9781108591034 · Cited by 857
Smooth Dynamics and New Theoretical Ideas in Nonequilibrium Statistical Mechanics
Ruelle, D. (1999) · Journal of Statistical Physics · doi:10.1023/a:1004593915069 · Cited by 438
Self-citationThe Metric Entropy of Diffeomorphisms: Part II: Relations between Entropy, Exponents and Dimension
Ledrappier, F., & Young, L.-S. (1985) · The Annals of Mathematics · doi:10.2307/1971329 · Cited by 361
Metadata
- Authors
- Ruelle, D.
- Venue
- Publications Mathématiques de l'IHÉS
- Publisher
- MathDoc/Centre Mersenne
- Published
- 1979-12-07
- Volume
- 50
- Pages
- 27-58
- ISSN
- 0073-8301 (ISSN-L)
- 1618-1913
- OpenAlex
- W2069824804
- Cited by
- 663
- References
- 0
- FWCI
- 13.57
- Type
- journal article
- Language
- en
- Open access
- closed
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- Ruelle, D. (1979). Ergodic theory of differentiable dynamical systems. Publications Mathématiques de l'IHÉS. https://doi.org/10.1007/bf02684768
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