Sydney Dynamics Group Seminar: Dr. Jason Atnip (UNSW) -- Sydney Dynamics group Seminar

Seminar : Sydney Dynamics group Seminar 
Day/time : Thursday, March 26 at 4:00 PM,
Location : SMRI seminar room (A12 Macleay Room 301) 
Speaker : Dr. Jason Atnip, UNSW 

Title: Conditional limit theorems for dynamical systems 

Abstract: In this talk we will consider an open dynamical system, that is, a dynamical
system where we have placed a hole of positive measure in phase space.  For chaotic
systems, the Birkhoff ergodic theorem implies that almost every point will eventually
"escape" through the hole.  On the other hand, there is also a (usually) fractal,
invariant subset of points which never escape through the hole, called the surviving
set.  Considering either the dynamics on the closed system (without a hole) or the open
system restricted to the surviving set, one can prove statistical limit laws relative to
the closed or open invariant measures respectively.  We seek to describe the statistical
properties of the dynamics of typical trajectories before they escape in finite time.
By considering a sequence of observations at points which survive for n-steps and using
spectral techniques, we are able to prove a host of conditional limit theorems for both
random and deterministic dynamical systems.