UW Rainwater Seminar
Winter 2011
Date: February 8 at 2:30
Location: UW
Padelford C-401
Speaker: Douglas Lind, University of Washington
Title: Periodic points and entropy
Abstract:
There is a general principle for algebraic dynamical systems that the
growth rate of periodic points should be the entropy. This has to be suitably
interpreted, and I will formulate a conjecture for which there are no known
counterexamples. For a single toral automorphism this is equivalent to a deep
result in diophantine approximation. For several commuting group automorphisms
the corresponding diophantine result is not known, but I will describe recent
work with Schmidt and Verbitskiy using homoclinic points which provides an
alternative approach in many cases. Understanding the limits of this approach
involves real algebraic geometry, and, surprisingly, even logic!