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Ergodic sums of non-integrable functions under one-dimensional dynamical systems with indifferent fixed points

Published online by Cambridge University Press:  09 March 2004

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 consider one-dimensional dynamical systems with indifferent fixed points (fixed points with derivative one). Many such maps have absolutely continuous ergodic infinite invariant measures. We study the limit of the ratio of the ergodic sum of fA to that of fB, where the integrals of fA and fB are infinite with respect to the absolutely continuous ergodic infinite invariant measure. If fA and fB are analytic functions on [0, 1], the result in this paper makes it clear whether the ratio of the ergodic sum of fA to that of fB converges in the Lebesgue measure or not.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 2 , April 2004 , pp. 525 - 545
Copyright
2004 Cambridge University Press

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