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Shadowing property of non-invertible maps with hyperbolic measures. (English) Zbl 0942.37008
Using a version of the Shadowing Lemma the author proves the following theorem and shows its consequences. $$M$$ is a smooth closed manifold. Theorem A: Let $$f:M \rightarrow M$$ be a $$C^{1+\alpha}$$ map ($$\alpha > 0$$). Suppose that $$f$$ has a non-atomic ergodic hyperbolic measure. Then there exists a hyperbolic horseshoe of $$f$$, and the topological entropy of $$f$$, $$h(f)$$, is positive.
Reviewer: J.Ombach (Kraków)

##### MSC:
 37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems 37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics
##### Keywords:
hyperbolic measure; horseshoe; topological entropy; shadowing
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