Equilibrium states for the classical Lorenz attractor and sectional-hyperbolic attractors in higher dimensions
| Autor: | Pacifico, Maria Jose, Yang, Fan, Yang, Jiagang |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | It has long been conjectured that the classical Lorenz attractor supports a unique measure of maximal entropy. In this article, we give a positive answer to this conjecture and its higher-dimensional counterpart by considering the uniqueness of equilibrium states for H\"older continuous functions on a sectional-hyperbolic attractor $\Lambda$. We prove that in a $C^1$-open and dense family of vector fields (including the classical Lorenz attractor), if the point masses at singularities are not equilibrium states, then there exists a unique equilibrium state supported on $\Lambda$. In particular, there exists a unique measure of maximal entropy for the flow $X|_\Lambda$. Comment: 96 pages, 10 figures. This version contains the classical Lorenz attractor as an example. To appear on Duke Math. J |
| Databáze: | arXiv |
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