Thermodynamic formalism for and hitting time statistics for random open dynamical systems

CDSNS Colloquium
Wednesday, May 8, 2024 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Jason Atnip – Queensland University –
Alex Blumenthal

Please Note: In this talk we present some recent results on thermodynamic formalism for random open dynamical systems. In particular, we poke random holes in the phase space and prove the existence of unique equilibrium states on the set of surviving points as well as find the rate at which mass escapes through these holes. If we consider small holes, through a perturbative approach, we are able to make a connection to extreme value theory and hitting time statistics. Furthermore, we prove a Gumbel's law and show that the distribution of multiple returns to small holes is asymptotically compound Poisson distributed.