Ergodic optimization for continuous functions on the Dyck-Motzkin shifts
| Autor: | Shinoda, Mao, Takahasi, Hiroki, Yamamoto, Kenichiro |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. The Dyck and Motzkin shifts are well-known examples of transitive subshifts over a finite alphabet that are not intrinsically ergodic. We show that the space of continuous functions on any Dyck-Motzkin shift splits into two subsets: one is a dense $G_\delta$ set with empty interior for which any maximizing measure has zero entropy; the other is contained in the closure of the set of functions having uncountably many, fully supported measures that are Bernoulli. One key ingredient of a proof of this result is the path connectedness of the space of ergodic measures of the Dyck-Motzkin shift. Comment: 22 pages, 2 figures |
| Databáze: | arXiv |
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