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Ergodic optimization of super-continuous functions on shift spaces

Published online by Cambridge University Press:  14 October 2011

ANTHONY QUAS  and
JASON SIEFKEN
ANTHONY QUAS
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria BC, Canada V8W 3R4 (email: aquas@uvic.ca, siefkenj@uvic.ca)
JASON SIEFKEN
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria BC, Canada V8W 3R4 (email: aquas@uvic.ca, siefkenj@uvic.ca)
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Abstract

Ergodic optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that ‘most’ functions are optimized by measures supported on a periodic orbit, and it has been proved in several separable spaces that an open and dense subset of functions is optimized by measures supported on a periodic orbit. All known positive results have been for separable spaces. We give in this paper the first positive result for a non-separable space, the space of super-continuous functions on the full shift, where the set of functions optimized by periodic orbit measures contains an open dense subset.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 6 , December 2012 , pp. 2071 - 2082
Copyright
Copyright © Cambridge University Press 2011

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