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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
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