Sensitive dependence of geometric Gibbs states at positive temperature
Abstract
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.
Keywords
Cite
@article{arxiv.1804.05681,
title = {Sensitive dependence of geometric Gibbs states at positive temperature},
author = {Daniel Coronel and Juan Rivera-Letelier},
journal= {arXiv preprint arXiv:1804.05681},
year = {2019}
}
Comments
Minor changes. arXiv admin note: substantial text overlap with arXiv:1708.03965, arXiv:1305.4971