Ergodic optimization for generic continuous functions | Zendy

Ian D. Morris | Zendy

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Ergodic optimization for generic continuous functions

Author(s) -

Ian D. Morris

Publication year - 2010

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2010.27.383

Subject(s) - ergodic theory , invariant measure , invariant (physics) , mathematics , residual , dynamical systems theory , pure mathematics , set (abstract data type) , discrete mathematics , computer science , physics , algorithm , mathematical physics , quantum mechanics , programming language

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 Bremont, 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.

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