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October  2007, 17(4): 891-900. doi: 10.3934/dcds.2007.17.891

The dynamical Borel-Cantelli lemma for interval maps

Dong Han Kim 1,

1. 

Department of Mathematics, The University of Suwon, San 2-2, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, South Korea

Received  February 2006 Revised  October 2006 Published  January 2007

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.
Keywords: maps with an indifferent fixed point., the dynamical Borel-Cantelli lemma.
Mathematics Subject Classification: Primary: 37A25, 37E0.
Citation: Dong Han Kim. The dynamical Borel-Cantelli lemma for interval maps. Discrete & Continuous Dynamical Systems, 2007, 17 (4) : 891-900. doi: 10.3934/dcds.2007.17.891
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