Tokyo Journal of Mathematics

Shadowing Property of Non-Invertible Maps with Hyperbolic Measures

Yong Moo CHUNG

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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.

Article information

Source
Tokyo J. Math., Volume 22, Number 1 (1999), 145-166.

Dates
First available in Project Euclid: 31 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1270041619

Digital Object Identifier
doi:10.3836/tjm/1270041619

Mathematical Reviews number (MathSciNet)
MR1692027

Zentralblatt MATH identifier
0942.37008

Citation

CHUNG, Yong Moo. Shadowing Property of Non-Invertible Maps with Hyperbolic Measures. Tokyo J. Math. 22 (1999), no. 1, 145--166. doi:10.3836/tjm/1270041619. https://projecteuclid.org/euclid.tjm/1270041619


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