Ergodic optimization of super-continuous functions on shift spaces

Anthony Quas*, Jason Siefken

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2071-2082
Number of pages12
JournalErgodic Theory and Dynamical Systems
Volume32
Issue number6
DOIs
StatePublished - Dec 2012

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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