Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-14T12:04:24.241Z Has data issue: false hasContentIssue false
  • English
  • Français

On the convergence to equilibrium states for certain non-hyperbolic systems

Published online by Cambridge University Press:  02 April 2001

MICHIKO YURI
MICHIKO YURI
Affiliation:
Department of Business Administration, Sapporo University, Nishioka, Toyohira-ku, Sapporo 062, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We study the convergence to equilibrium states forcertain non-hyperbolic piecewise invertible systems.The multi-dimensional maps we shall considerdo not satisfy Renyi's condition (uniformlybounded distortion for any iterates) and do not necessarilysatisfy the Markov property.The failure of both conditions may cause singularities ofdensities of the invariant measures, even if they arefinite, and causes a crucial difficulty in applying thestandard technique of the Perron–Frobeniusoperator. Typical examples of maps we consideradmit indifferent periodic orbits and arise in many contexts.For the convergence of iterates ofthe Perron–Frobenius operator,we study continuity of the invariant density.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 4 , August 1997, pp. 977 - 1000
Copyright
© 1997 Cambridge University Press