### 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 original | English |
---|---|

Páginas (desde-hasta) | 383-425 |

Número de páginas | 43 |

Publicación | Communications in Mathematical Physics |

Volumen | 368 |

N.º | 1 |

DOI | |

Estado | Published - 1 may 2019 |

### Huella dactilar

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Citar esto

*Communications in Mathematical Physics*,

*368*(1), 383-425. https://doi.org/10.1007/s00220-019-03350-6

}

*Communications in Mathematical Physics*, vol. 368, n.º 1, pp. 383-425. https://doi.org/10.1007/s00220-019-03350-6

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

Resultado de la investigación: Article

TY - JOUR

T1 - Sensitive Dependence of Geometric Gibbs States at Positive Temperature

AU - Coronel, Daniel

AU - Rivera-Letelier, Juan

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85065171444&partnerID=8YFLogxK

U2 - 10.1007/s00220-019-03350-6

DO - 10.1007/s00220-019-03350-6

M3 - Article

AN - SCOPUS:85065171444

VL - 368

SP - 383

EP - 425

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -