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

David M. McClendon

doi:10.3934/dcdss.2009.2.251

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2009, Volume 2, Issue 2: 251-268. Doi: 10.3934/dcdss.2009.2.251

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

David M. McClendon^1,

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

Received: June 30, 2008

Revised: October 31, 2008

Published: May 2009

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Abstract

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''.

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Mathematics Subject Classification: Primary: 37A99; Secondary: 37A40, 37B99.

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