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Ergodic theory of differentiable dynamical systems

  • David Ruelle
Article

Abstract

Iff is a C1 + ɛ diffeomorphism of a compact manifold M, we prove the existence of stable manifolds, almost everywhere with respect to everyf-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.

Keywords

Tangent Space Ergodic Theory Stable Manifold Ergodic Theorem Characteristic Exponent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Publications mathématiques de l’I.H.É.S 1979

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  • David Ruelle

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