Phase transitions for surface diffeomorphisms

Thiago Bomfim; Paulo Varandas

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arXiv · 2301.10238

Phase transitions for surface diffeomorphisms

Thiago Bomfim·Paulo Varandas

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Abstract

In this paper we consider $C^1$ surface diffeomorphisms and study the existence of phase transitions, here expressed by the non-analiticity of the pressure function associated to smooth and geometric-type potentials. We prove that the space of $C^1$-surface diffeomorphisms admitting phase transitions is a $C^1$-Baire generic subset of the space of non-Anosov diffeomorphisms. In particular, if $S$ is a compact surface which is not homeomorphic to the 2-torus then a $C^1$-generic diffeomorphism on $S$ has phase transitions. We obtain similar statements in the context of $C^1$--volume preserving diffeomorphisms. Finally, we prove that a $C^2$-surface diffeomorphism exhibiting a dominated splitting admits phase transitions if and only if has some non-hyperbolic periodic point.

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Thiago Bomfim, Paulo Varandas. 2023-01-24. Phase transitions for surface diffeomorphisms. https://arxiv.org/abs/2301.10238

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