Hitting and return times in ergodic dynamical systems

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dc.creatorHaydn, N.
dc.creatorLacroix, Y.
dc.creatorVaienti, S.
dc.date2004-10-18
dc.date.accessioned2026-07-07T05:13:22Z
dc.date.available2026-07-07T05:13:22Z
dc.descriptionGiven an ergodic dynamical system $(X,T,μ)$, and $U\subset X$ measurable with $μ(U)>0$, let $μ(U)τ_U(x)$ denote the normalized hitting time of $x\in X$ to $U$. We prove that given a sequence $(U_n)$ with $μ(U_n)\to 0$, the distribution function of the normalized hitting times to $U_n$ converges weakly to some sub-probability distribution $F$ if and only if the distribution function of the normalized return time converges weakly to some distribution function $\tilde F$, and that in the converging case, $$ F(t)=\int_0^t(1-\tilde F(s))ds, t\ge 0.\tag$\diamondsuit$ $$ This in particular characterizes asymptotics for hitting times, and shows that the asymptotics for return times is exponential if and only if the one for hitting times is too.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0410384
dc.identifierhttp://arxiv.org/abs/math/0410384
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72916
dc.subjectDynamical Systems
dc.subjectProbability
dc.subject37A05;37A50;28D05
dc.titleHitting and return times in ergodic dynamical systems
dc.typetext

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