## EVENT DETAILS AND ABSTRACT

**Colloquium**
**Title:** Where to Place a Hole to Achieve a Maximal Escape Rate

**Speaker:** Professor Leonid Bunimovich

**Speaker Info:** Georgia Tech

**Brief Description:**

**Special Note**:

**Abstract:**

A natural question of how the survival probability depends upon a position
of the hole was seemingly never addressed in the theory of open dynamical
systems.
This dependence occurred to be very essential for some strongly chaotic
(uniformly hyperbolic) systems. It is closely related to the distribution of
periodic orbits. It seems obvious that the bigger the hole is the faster is
the escape through that hole. However, generally it is not true, and some
properties of dynamics may play a role comparable to the size of the hole.
The main result is valid for all finite times (starting with some moment)
which is unusual in dynamical systems theory where typically statements are
asymptotic when time tends to infinity. Such finite time results may have
many applications as the problem in the title has by itself.

**Date:** Thursday, April 09, 2009

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Prof. Jeff Xia

**Contact email:** xia@math.northwestern.edu

**Contact Phone:** 847-491-5487

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