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arXiv · 2607.09394

On the Abundance of Phase Transitions in Dynamical Systems

Alexander Arbieto·Walter Britto·Elias Rego
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Abstract

In this work, we investigate the mechanisms that trigger phase transitions in both discrete-time and continuous-time dynamical systems. We prove a simple topological condition that implies the existence of H\"older continuous potentials displaying phase transitions. As a consequence, we show that phase transitions are typical in several scenarios. Specifically, for $C^1$ diffeomorphisms and $C^1$ vector fields, we show that phase transitions are generic among non-transitive systems. In low dimensions, we conclude that they are generic for non-Anosov systems. Finally, in the $C^0$ setting, we prove that on any compact topological manifold of dimension different from 4, there exists a dense set of homeomorphisms with finite entropy that display phase transitions.

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Alexander Arbieto, Walter Britto, Elias Rego. 2026-07-10. On the Abundance of Phase Transitions in Dynamical Systems. https://arxiv.org/abs/2607.09394

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