Idempotent approach to level-2 variational principles in Thermodynamical Formalism
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914959804334080 |
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| author | Lopes, A. O. Mengue, J. K. Oliveira, E. R. |
| author_facet | Lopes, A. O. Mengue, J. K. Oliveira, E. R. |
| contents | In this work we introduce an idempotent pressure to level-2 functions and its associated density entropy. All this is related to idempotent pressure functions which is the natural concept that corresponds to the meaning of probability in the level-2 max-plus context. In this general framework the equilibrium states, maximizing the variational principle, are not unique. We investigate the connections with the general convex pressure introduced recently to level-1 functions by Biś, Carvalho, Mendes and Varandas. Our general setting contemplates the dynamical and not dynamical framework. We also study a characterization of the density entropy in order to get an idempotent pressure invariant by dynamical systems acting on probabilities; this is therefore a level-2 result. We are able to produce idempotent pressure functions at level-2 which are invariant by the dynamics of the pushforward map via a form of Ruelle operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19203 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Idempotent approach to level-2 variational principles in Thermodynamical Formalism Lopes, A. O. Mengue, J. K. Oliveira, E. R. Dynamical Systems Mathematical Physics In this work we introduce an idempotent pressure to level-2 functions and its associated density entropy. All this is related to idempotent pressure functions which is the natural concept that corresponds to the meaning of probability in the level-2 max-plus context. In this general framework the equilibrium states, maximizing the variational principle, are not unique. We investigate the connections with the general convex pressure introduced recently to level-1 functions by Biś, Carvalho, Mendes and Varandas. Our general setting contemplates the dynamical and not dynamical framework. We also study a characterization of the density entropy in order to get an idempotent pressure invariant by dynamical systems acting on probabilities; this is therefore a level-2 result. We are able to produce idempotent pressure functions at level-2 which are invariant by the dynamics of the pushforward map via a form of Ruelle operator. |
| title | Idempotent approach to level-2 variational principles in Thermodynamical Formalism |
| topic | Dynamical Systems Mathematical Physics |
| url | https://arxiv.org/abs/2409.19203 |