Phase diagram for intermittent maps

Abstract

We explore the phase diagram for potentials in the space of H\"older continuous functions of a given exponent and for the dynamical system generated by a Pomeau--Manneville, or intermittent, map. There is always a phase where the unique Gibbs state exhibits intermittent behavior. It is the only phase for a specific range of values of the H\"older exponent. For the remaining values of the H\"older exponent, a second phase with stationary behavior emerges. In this case, a co-dimension 1 submanifold separates the intermittent and stationary phases. It coincides with the set of potentials at which the pressure function fails to be real-analytic. We also describe the relationship between the phase transition locus, (persistent) phase transitions in temperature, and ground states.