An Ambrose-Kakutani representation theorem for countable-to-1 semiflows

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June 2009, 2(2): 251-268. doi: 10.3934/dcdss.2009.2.251

An Ambrose-Kakutani representation theorem for countable-to-1 semiflows

1.	Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2370, United States

Received July 2008 Revised November 2008 Published April 2009

Abstract
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Let $X$ be a Polish space and $T_t$ a jointly Borel measurable action of $\mathbb{R}^+ = [0, \infty)$ on $X$ by surjective maps preserving some Borel probability measure $\mu$ on $X$. We show that if each $T_t$ is countable-to-1 and if $T_t$ has the "discrete orbit branching property'' (described in the introduction), then $(X, T_t)$ is isomorphic to a "semiflow under a function''.

Keywords: suspension semiflow., measure-preserving semiflow, Borel semiflow.

Mathematics Subject Classification: Primary: 37A99; Secondary: 37A40, 37B9.

Citation: David M. McClendon. An Ambrose-Kakutani representation theorem for countable-to-1 semiflows. Discrete & Continuous Dynamical Systems - S, 2009, 2 (2) : 251-268. doi: 10.3934/dcdss.2009.2.251

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