The dynamical Borel-Cantelli lemma for interval maps

Dong Han Kim

doi:10.3934/dcds.2007.17.891

The dynamical Borel-Cantelli lemma for interval maps

Dong Han Kim

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

The dynamical Borel-Cantelli lemma for some interval maps is considered. For expanding maps whose derivative has bounded variation, any sequence of intervals satisfies the dynamical Borel-Cantelli lemma. If a map has an indifferent fixed point, then the dynamical Borel-Cantelli lemma does not hold even in the case that the map has a finite absolutely continuous invariant measure and summable decay of correlations.

Original language	English
Pages (from-to)	891-900
Number of pages	10
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	17
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2007.17.891
State	Published - Apr 2007

Keywords

Maps with an indifferent fixed point
The dynamical Borel-Cantelli lemma

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10.3934/dcds.2007.17.891

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title = "The dynamical Borel-Cantelli lemma for interval maps",

abstract = "The dynamical Borel-Cantelli lemma for some interval maps is considered. For expanding maps whose derivative has bounded variation, any sequence of intervals satisfies the dynamical Borel-Cantelli lemma. If a map has an indifferent fixed point, then the dynamical Borel-Cantelli lemma does not hold even in the case that the map has a finite absolutely continuous invariant measure and summable decay of correlations.",

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AB - The dynamical Borel-Cantelli lemma for some interval maps is considered. For expanding maps whose derivative has bounded variation, any sequence of intervals satisfies the dynamical Borel-Cantelli lemma. If a map has an indifferent fixed point, then the dynamical Borel-Cantelli lemma does not hold even in the case that the map has a finite absolutely continuous invariant measure and summable decay of correlations.

KW - Maps with an indifferent fixed point

KW - The dynamical Borel-Cantelli lemma

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DO - 10.3934/dcds.2007.17.891

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 4

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The dynamical Borel-Cantelli lemma for interval maps

Abstract

Keywords

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