Phase transitions in temperature for intermittent maps
Daniel Coronel, Juan Rivera-Letelier
TL;DR
This work characterizes when phase transitions in temperature occur for a restricted, regular class of Hölder-type potentials on the Manneville–Pomeau map and how robustness emerges from ergodic optimization. By building a Bowen-type framework via an inducing scheme and a two-variable pressure, it reduces the global thermodynamic problem to a finite-approximation condition tied to the unique maximizing measure at the indifferent fixed point, δ0. The main contribution is an equivalence: a phase transition in temperature is present iff δ0 is the unique maximizing measure, and this relation defines an open set in the potential space; in the borderline case γ=α the leading coefficient governs robustness and rigidity. The paper also provides a detailed inducing- and transfer-operator toolkit, yielding concrete consequences for the geometric potential and for general ω-typical Hölder potentials, and it connects the phase diagram to ergodic optimization. Together with a companion paper addressing Hölder potentials in full generality, these results advance the understanding of phase transitions in intermittent dynamical systems and their sensitivity to the interaction space.
Abstract
This article characterizes phase transitions in temperature within a specific space of Hölder continuous potentials, distinguished by their regularity and asymptotic behavior at zero. We also characterize the phase transitions in temperature that are robust within this space. Our results reveal a connection between phase transitions in temperature and ergodic optimization.