February  2010, 27(1): 383-388. doi: 10.3934/dcds.2010.27.383

Ergodic optimization for generic continuous functions

1. 

Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom

Received  June 2009 Revised  December 2009 Published  February 2010

Given a real-valued continuous function $f$ defined on the phase space of a dynamical system, an invariant measure is said to be maximizing if it maximises the integral of $f$ over the set of all invariant measures. Extending results of Bousch, Jenkinson and Brémont, we show that the ergodic maximizing measures of functions belonging to a residual subset of the continuous functions may be characterised as those measures which belong to a residual subset of the ergodic measures.
Citation: Ian D. Morris. Ergodic optimization for generic continuous functions. Discrete & Continuous Dynamical Systems - A, 2010, 27 (1) : 383-388. doi: 10.3934/dcds.2010.27.383
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