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Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds

This work is a part of a M.Sc. thesis at the Weizmann Institute of Science. The author was partly supported by the ISF grant 199/14.
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  • We construct countable Markov partitions for non-uniformly hyperbolic diffeomorphisms on compact manifolds of any dimension, extending earlier work of Sarig [29] for surfaces. These partitions allow us to obtain symbolic coding on invariant sets of full measure for all hyperbolic measures whose Lyapunov exponents are bounded away from zero by a fixed constant. Applications include counting results for hyperbolic periodic orbits, and structure of hyperbolic measures of maximal entropy.

    Mathematics Subject Classification: Primary: 37D25; Secondary: 37B10.


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  • Figure 1.  Illustration of the discussed tangent vectors

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