Ergodic theory of differentiable dynamical systems

  • David Ruelle


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.


Tangent Space Ergodic Theory Stable Manifold Ergodic Theorem Characteristic Exponent 
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  • David Ruelle

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