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Diffeomorphisms with positive entropy and chaos in the sense of Li–Yorke

Published online by Cambridge University Press:  22 September 2003

NAOYA SUMI
NAOYA SUMI
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo, 192-0397, Japan (e-mail: sumi@comp.metro-u.ac.jp)
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Abstract

We show that if f is a C^2 diffeomorphism with positive entropy on an n-dimensional closed manifold (n \geq 2) then f is chaotic in the sense of Li–Yorke, and moreover f is \ast-chaotic on the closure of the stable manifold for some point. The notion of ‘\ast-chaos’ was introduced by Kato in relation to Li–Yorke's chaos in the context of topological dynamics.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 2 , April 2003 , pp. 621 - 635
Copyright
2003 Cambridge University Press

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