Sensitive Dependence of Geometric Gibbs States at Positive Temperature

Daniel Coronel, Juan Rivera-Letelier

Resultado de la investigación: Article

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

Huella dactilar

Gibbs States
Enter
Thermodynamic Formalism
temperature
trucks
statistical mechanics
Statistical Mechanics
Open set
formalism
Converge
thermodynamics
Family

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Citar esto

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Sensitive Dependence of Geometric Gibbs States at Positive Temperature. / Coronel, Daniel; Rivera-Letelier, Juan.

En: Communications in Mathematical Physics, Vol. 368, N.º 1, 01.05.2019, p. 383-425.

Resultado de la investigación: Article

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