1 3 A pr 2 00 8 THE DYNAMICAL BOREL - CANTELLI LEMMA AND THE WAITING TIME PROBLEMS
نویسنده
چکیده
We investigate the connection between the dynamical Borel-Cantelli and waiting time results. We prove that if a system has the dynamical BorelCantelli 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.
منابع مشابه
ar X iv : m at h / 06 10 21 3 v 1 [ m at h . D S ] 6 O ct 2 00 6 THE DYNAMICAL BOREL - CANTELLI LEMMA AND THE WAITING TIME PROBLEMS
We investigate the connection between the dynamical Borel-Cantelli and waiting time results. We prove that if a system has the dynamical BorelCantelli 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 decreasi...
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