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Sojourn times in small neighborhoods of indifferent fixed points of one-dimensional dynamical systems

Published online by Cambridge University Press:  01 February 2000

TOMOKI INOUE
TOMOKI INOUE
Affiliation:
Division of Applied Mathematics, Department of Electrical and Electronic Engineering, Faculty of Engineering, Ehime University, Matsuyama, 790-8577, Japan
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Abstract

We study one-dimensional dynamical systems with indifferent fixed points $p$ and $q$. The dynamical systems we study in this paper have ergodic, infinite, invariant measures. We consider the limit of the ratio of the sojourn time of the trajectory in a small neighborhood of $p$ to that in a small neighborhood of $q$. We show that the limit does not exist under some conditions, which has been announced in a previous paper. In fact we prove that the limit supreme of the ratio is $\infty$ and that the limit infimum is 0.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 1 , February 2000 , pp. 241 - 257
Copyright
2000 Cambridge University Press

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