Sensitive Dependence of Geometric Gibbs States at Positive Temperature

Daniel Coronel, Juan Rivera-Letelier

Resultado de la investigación: Contribución a una revistaArtículo

Resumen

We give the first example of a smooth family of real and complex maps having sensitive dependence of geometric Gibbs states at positive temperature. This family consists of quadratic-like maps that are non-uniformly hyperbolic in a strong sense. We show that for a dense set of maps in the family the geometric Gibbs states do not converge at positive temperature. These are the first examples of non-convergence at positive temperature in statistical mechanics or the thermodynamic formalism, and answers a question of van Enter and Ruszel. We also show that this phenomenon is robust: There is an open set of analytic 2-parameter families of quadratic-like maps that exhibit sensitive dependence of geometric Gibbs states at positive temperature.

Idioma originalInglés
Páginas (desde-hasta)383-425
Número de páginas43
PublicaciónCommunications in Mathematical Physics
Volumen368
N.º1
DOI
EstadoPublicada - 1 may 2019

Áreas temáticas de ASJC Scopus

  • Física estadística y no lineal
  • Física matemática

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