Dynamical Systems Seminar

Open random dynamics and return time statistics

Name: Open random dynamics and return time statistics
Start: 2023-10-17T17:00:00+02:00
End: 2023-10-17T18:00:00+02:00
Location: SNS - Centro De Giorgi

by Jason Atnip (University of Queensland)

Tuesday 17 Oct 2023, 17:00 → 18:00 Europe/Rome

SNS - Centro De Giorgi

Description

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.