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Ergodic optimization for generic continuous functions
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Morris, Ian D. (2010) Ergodic optimization for generic continuous functions. Discrete and Continuous Dynamical Systems, Vol.27 (No.1). pp. 383-388. doi:10.3934/dcds.2010.27.383 ISSN 1078-0947.
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Official URL: http://dx.doi.org/10.3934/dcds.2010.27.383
Abstract
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.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Discrete and Continuous Dynamical Systems | ||||
| Publisher: | American Institute of Mathematical Sciences | ||||
| ISSN: | 1078-0947 | ||||
| Official Date: | May 2010 | ||||
| Dates: |
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| Volume: | Vol.27 | ||||
| Number: | No.1 | ||||
| Number of Pages: | 6 | ||||
| Page Range: | pp. 383-388 | ||||
| DOI: | 10.3934/dcds.2010.27.383 | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
| Grant number: | EP/E020801/1 (EPSRC) |
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