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| Titel: |
Ergodic optimization for noncompact dynamical systems |
| Auteur: |
Jenkinson, O. Mauldin, R. D. Urbanski, M. |
| Verschenen in: |
Dynamical systems |
| Paginering: | Jaargang 22 (2007) nr. 3 pagina's 379-388 |
| Jaar: |
2007-09 |
| Inhoud: |
The purpose of this note is to initiate the study of ergodic optimization for general topological dynamical systems T:X→ X, where the topological space X need not be compact. Given [image omitted], four possible notions of largest ergodic average are defined; for compact metrisable X these notions coincide, while for general Polish spaces X they are related by inequalities, each of which may be strict. We seek conditions on f which guarantee the existence of a normal form, in order to characterize its maximizing measures in terms of their support. For compact metrisable X it suffices to find a fixed point form. For general Polish X this is not the case, but an extra condition on f, essential compactness, is shown to imply the existence of a normal form. When T:X→ X is the full shift on a countable alphabet, essential compactness yields an easily checkable criterion for the existence of a normal form. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 2 van 8 gevonden artikelen
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