The compound Poisson distribution and return times in dynamical systems

Details The compound Poisson distribution and return times in dynamical systems The compound Poisson distribution and return times in dynamical systems

2008-04-07

arxiv.org/abs/0804.1032v1

Mathematics

Dynamical Systems

18 pages

Scientific paper

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 general theorem that can be used to establish compound Poisson distributions in many other settings.

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