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June 1999 Shadowing Property of Non-Invertible Maps with Hyperbolic Measures
Yong Moo CHUNG
Tokyo J. Math. 22(1): 145-166 (June 1999). DOI: 10.3836/tjm/1270041619

Abstract

We show that if a differentiable map of a smooth manifold has a non-atomic ergodic hyperbolic measure then the topological entropy is positive and the space contains a hyperbolic horseshoe. Moreover we give some relations between hyperbolic measures and periodic points for differentiable maps. These are generalized contents of the results obtained by Katok for diffeomorphisms.

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Yong Moo CHUNG. "Shadowing Property of Non-Invertible Maps with Hyperbolic Measures." Tokyo J. Math. 22 (1) 145 - 166, June 1999. https://doi.org/10.3836/tjm/1270041619

Information

Published: June 1999
First available in Project Euclid: 31 March 2010

zbMATH: 0942.37008
MathSciNet: MR1692027
Digital Object Identifier: 10.3836/tjm/1270041619

Rights: Copyright © 1999 Publication Committee for the Tokyo Journal of Mathematics

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Vol.22 • No. 1 • June 1999
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