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Markov covers and finiteness of periodic attractors for diffeomorphisms with a dominated splitting

Published online by Cambridge University Press:  01 February 2000

MASAYUKI ASAOKA
MASAYUKI ASAOKA
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan (e-mail: asaoka@kusm.kyoto-u.ac.jp) Current address: Department of Mathematical and Natural Sciences, Faculty of Integrated Arts & Sciences, The University of Tokushima, Minami-Josanjima 1-1, Tokushima 770-8502, Japan (e-mail: asaoka@ias.tokushima-u.ac.jp)
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Abstract

In this paper, we show the existence of Markov covers for $C^2$ surface diffeomorphisms with a dominated splitting under some assumptions. Using a Markov cover, we can reduce the dynamics to a one-dimensional dynamical system having a good metric property. As an application, we show finiteness of periodic attractors for the above diffeomorphisms.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 1 , February 2000 , pp. 1 - 14
Copyright
2000 Cambridge University Press

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