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arXiv · 2608.12784

Thermodynamic formalism for intermittent maps with multiple neutral fixed points and phase transitions

Daniel Coronel·Francisco Monardes
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Abstract

In this paper, we develop the thermodynamic formalism for intermittent full-branch interval maps with finitely many neutral fixed points and for a broad class of possibly discontinuous potentials. Under a hyperbolicity assumption on the potential, we prove the existence of a unique equilibrium state with positive entropy and exponential decay of correlations. Furthermore, we characterize the phase transitions for the one-parameter family $\beta\varphi$, with $\beta>0$, and prove that, at the critical parameter, multiple ergodic equilibrium states may coexist, at most one of which has positive entropy. Our approach relies on a detailed analysis of conformal measures.

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Daniel Coronel, Francisco Monardes. 2026-08-13. Thermodynamic formalism for intermittent maps with multiple neutral fixed points and phase transitions. https://arxiv.org/abs/2608.12784

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