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

Ergodic optimization for generic continuous functions

Ian D. Morris 1,

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.
Keywords: maximizing measure., Ergodic optimization.
Mathematics Subject Classification: Primary: 37A99; Secondary: 37D20, 37E1.
Citation: Ian D. Morris. Ergodic optimization for generic continuous functions. Discrete & Continuous Dynamical Systems, 2010, 27 (1) : 383-388. doi: 10.3934/dcds.2010.27.383
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