The dynamical Borel-Cantelli lemma and the waiting time problems

• Autores: Stefano Galatolo, Dong Han Kim
• Localización: Indagationes mathematicae, ISSN 0019-3577, Vol. 18, Nº 3, 2007, págs. 421-434
• Idioma: inglés
• DOI: 10.1016/s0019-3577(07)80031-0
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• Resumen

  • We investigate the connection between the dynamical Borel-Cantelli and waiting time results. We prove that if a system has the dynamical Borel-Cantelli property, then the time needed to enter for the first time in a sequence of small balls scales as the inverse of the measure of the balls. Conversely if we know the waiting time behavior of a system we can prove that certain sequences of decreasing balls satisfies the Borel-Cantelli property. This allows to obtain Borel-Cantelli like results in systems like axiom A and generic interval exchanges.