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- W4297821000 abstract "It is known that all uniformly expanding or hyperbolic dynamics have no phase transition with respect to Holder continuous potentials. In cite{BC21}, is proved that for all transitive $C^{1+alpha}-$local diffeomorphism $f$ on the circle, that is neither a uniformly expanding map nor invertible, has a unique thermodynamic phase transition with respect to the geometric potential, in other words, the topological pressure function $mathbb{R} ni t mapsto P_{top}(f,-tlog|Df|)$ is analytic except at a point $t_{0} in (0 , 1]$. Also it is proved spectral phase transitions, in other words, the transfer operator $mathcal{L}_{f,-tlog|Df|}$ acting on the space of Holder continuous functions, has the spectral gap property for all $t<t_0$ and does not have the spectral gap property for all $tgeq t_0$. Our goal is to prove that the results of thermodynamical and spectral phase transitions imply a multifractal analysis for the Lyapunov spectrum. In particular, we exhibit a class of partially hyperbolic endomorphisms that admit thermodynamical and spectral phase transitions with respect to the geometric potential, and we describe the multifractal analysis of your central Lyapunov spectrum." @default.
- W4297821000 created "2022-10-01" @default.
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- W4297821000 date "2022-09-12" @default.
- W4297821000 modified "2023-09-23" @default.
- W4297821000 title "From thermodynamic and spectral phase transitions to multifractal analysis" @default.
- W4297821000 doi "https://doi.org/10.48550/arxiv.2209.05590" @default.
- W4297821000 hasPublicationYear "2022" @default.
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