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.
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Dedicated to the memory of Rufus Bowen
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Ruelle, D. Ergodic theory of differentiable dynamical systems. Publications Mathématiques de L’Institut des Hautes Scientifiques 50, 27–58 (1979). https://doi.org/10.1007/BF02684768
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DOI: https://doi.org/10.1007/BF02684768