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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
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Abstract

We study the convergence to equilibrium states for certain non-hyperbolic piecewise invertible systems. The multi-dimensional maps we shall consider do not satisfy Renyi's condition (uniformly bounded distortion for any iterates) and do not necessarily satisfy the Markov property. The failure of both conditions may cause singularities of densities of the invariant measures, even if they are finite, and causes a crucial difficulty in applying the standard technique of the Perron–Frobenius operator. Typical examples of maps we consider admit indifferent periodic orbits and arise in many contexts. For the convergence of iterates of the Perron–Frobenius operator, we study continuity of the invariant density.

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

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