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2007, Volume 17, Issue 4: 891-900. Doi: 10.3934/dcds.2007.17.891
This issue Previous Article Global existence of weak solutions for Landau-Lifshitz-Maxwell equations Next Article On some dynamical systems in finite fields and residue rings

The dynamical Borel-Cantelli lemma for interval maps

  • 1.

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

Received:  January 31, 2006
Revised:  September 30, 2006
Published:  September 2007
Abstract Related Papers Cited by
    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.
    Mathematics Subject Classification: Primary: 37A25, 37E05.

    Citation:
    shu

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