Chung, Yong Moo Shadowing property of non-invertible maps with hyperbolic measures. (English) Zbl 0942.37008 Tokyo J. Math. 22, No. 1, 145-166 (1999). 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) Cited in 12 Documents 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 PDFBibTeX XMLCite \textit{Y. M. Chung}, Tokyo J. Math. 22, No. 1, 145--166 (1999; Zbl 0942.37008) Full Text: DOI