EVENT DETAILS AND ABSTRACT

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.