Low-temperature phase transitions in the quadratic family

2012/05/08 by Daniel Coronel, Coronel, Daniel, Juan Rivera‐Letelier +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1205.1833

openalex publication_date 2012/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give the first example of a quadratic map having a phase transition after the first zero of the geometric pressure function. This implies that several dimension spectra and large deviation rate functions associated to this map are not (expected to be) real analytic, in contrast to the uniformly hyperbolic case. The quadratic map we study has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense.

Citations

• High-order phase transitions in the quadratic family
• Recurrence times and rates of mixing

Cited by

• Density of spectral gap property for positively expansive dynamics and smooth potentials, with applications to the phase transition problem

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