منابع مشابه
The compound Poisson distribution and return times in dynamical systems
Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the limiting distribution is a compound Poissonian distribution. We also derive error terms for the convergence to the limiting distribution. We also prove a very ge...
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Foreword The last nine months of my study were dedicated to writing this master thesis. After having determined that I wanted it to be based on the course of Ergodic Theory, that I took in the first semester of the academic year 2003/2004, Karma Dajani suggested the subject of repetitions in number expansions. The subject interested me right from the start. Since in general writing my master th...
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We study returns in dynamical systems: when a set of points, initially populating a prescribed region, swarms around phase space according to a deterministic rule of motion, we say that the return of the set occurs at the earliest moment when one of these points comes back to the original region. We describe the statistical distribution of these “first–return” times in various settings: when ph...
متن کاملImproved Range in the Return times Theorem
We prove that the Return Times Theorem holds true for pairs of L − L functions, whenever 1 p + 1 q < 3 2
متن کاملPoincare Return times as Universal Sequences
Let (X, 36, m) be a probability space and let x be any invertible measure-preserving transformation of X. Given A, Bs 08, the Poincare return time sequence is the sequence of whole numbers n(A,B) = (neZ: m(A n zB) > 0). There is also a related point return time sequence, given for xeX and A €08 by n(x,A) = (neZ: xxsA). A Poincare return time sequence is the democratic version of the point retur...
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ژورنال
عنوان ژورنال: Dynamical Systems
سال: 2013
ISSN: 1468-9367,1468-9375
DOI: 10.1080/14689367.2013.822459