Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T13:34:35.375Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]) 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: [email protected])
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)