Dynamical Systems Seminar

Open random dynamics and return time statistics

by Jason Atnip (University of Queensland)

SNS - Centro De Giorgi

SNS - Centro De Giorgi


 In this talk we discuss recent results concerning the return time statistics for deterministic and random dynamical systems. Taking a perturbative approach, we consider a decreasing sequence of holes in phase space which shrink to a point. For systems satisfying a spectral gap, we show that limiting distribution of return times to these shrinking holes is a compound Poisson distribution. We provide specific examples of classes of transformations for which the limiting distribution is Polya-Aeppli.