TY - JOUR

T1 - Occupation times of sets of infinite measure for ergodic transformations

AU - Aaronson, Jon

AU - Thaler, Maximilian

AU - Zweimüller, Roland

PY - 2005/8

Y1 - 2005/8

N2 - Assume that T is a conservative ergodic measure-preserving transformation of the infinite measure space (X, A, μ). We study the asymptotic behaviour of occupation times of certain subsets of infinite measure. Specifically, we prove a Darling-Kac type distributional limit theorem for occupation times of barely infinite components which are separated from the rest of the space by a set of finite measure with continued-fraction (CF)-mixing return process. In the same setup we show that the ratios of occupation times of two components separated in this way diverge almost everywhere. These abstract results are illustrated by applications to interval maps with indifferent fixed points.

AB - Assume that T is a conservative ergodic measure-preserving transformation of the infinite measure space (X, A, μ). We study the asymptotic behaviour of occupation times of certain subsets of infinite measure. Specifically, we prove a Darling-Kac type distributional limit theorem for occupation times of barely infinite components which are separated from the rest of the space by a set of finite measure with continued-fraction (CF)-mixing return process. In the same setup we show that the ratios of occupation times of two components separated in this way diverge almost everywhere. These abstract results are illustrated by applications to interval maps with indifferent fixed points.

UR - http://www.scopus.com/inward/record.url?scp=23444460675&partnerID=8YFLogxK

U2 - 10.1017/S0143385704001051

DO - 10.1017/S0143385704001051

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AN - SCOPUS:23444460675

SN - 0143-3857

VL - 25

SP - 959

EP - 976

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 4

ER -