## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** On the identification of points by Borel semiflows

**Speaker:** David McClendon

**Speaker Info:** Northwestern University

**Brief Description:**

**Special Note**:

**Abstract:**

Let $X$ be a standard Polish space and $T_t$ a Borel measure-preserving semiflow on $X$. Say that two distinct points $x$ and $y$ are ``instantaneously discontinuously identified'' (IDI) by the semiflow if $T_t(x) = T_t(y)$ for all $t > 0$. The existence of such points is the only obstacle to representing the semiflow as a shift map on a space of continuous paths. We define the concept of ``orbit discontinuity'', a generalization of IDI, and discuss results regarding the structure and prevalence of such behavior. We explain how these results can be used to ``universally model'' Borel m.p. semiflows as shifts on a space of left-continuous paths.

**Date:** Tuesday, October 10, 2006

**Time:** 3:00pm

**Where:** Lunt 105

**Contact Person:** Prof. Bryna Kra

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

**Contact Phone:** 847-491-3013

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