## EVENT DETAILS AND ABSTRACT

**Colloquium**
**Title:** Entropy and Orbit Equivalence in Ergodic Theory

**Speaker:** Professor Daniel Rudolph

**Speaker Info:** Colorado Sate University

**Brief Description:**

**Special Note**:

**Abstract:**

I will first offer an overview of two core areas in
the dynamics of probability measure preserving dynamical systems, the
Kolmogorov-Sinai
theory of entropy and the Dye theory of orbit equivalence. Entropy is a
nontrivial
invariant that, said simply, measures the exponential growth rate of the
number of orbits in a dynamical system, a very rough measure of the
complexity of the orbit structure. On the other hand, the core theorem of
the orbit theory of these systems, due to Henry Dye, says that any two
free and ergodic systems are orbit equivalent, that is to say can be regarded
as sitting on the same set of orbits. Starting from the seeming conflict
between
these two notions we will build a revision of Dye's result that precisely
accounts
for entropy.

**Date:** Wednesday, April 13, 2005

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Prof. Elton P. Hsu

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

**Contact Phone:** 847-491-8541

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