Abstract:We study the behavior of the pressure function for Hölder continuous potentials on mixing subshifts of finite type. The classical theory of thermodynamic formalism shows that such pressure functions are convex, analytic and have slant asymptotes. We provide a sharp exponential lower bound on how fast the pressure function approaches its asymptotes. As a counterpart, we also show that there is no corresponding upper bound by exhibiting systems for which the convergence is arbitrarily slow. However, we prove that the exponential upper bound still holds for a generic Hölder potential. In addition, we determine that the pressure function satisfies a coarse uniform convexity property. Asymptotic bounds and quantitative convexity estimates are the first additional general properties of the pressure function obtained in the settings of Bowen and Ruelle since their groundbreaking work more than 40 years ago.
From: Tamara Kucherenko [view email]
[v1]
Tue, 28 Feb 2023 18:38:44 UTC (27 KB)
[v2]
Wed, 17 Jun 2026 15:14:00 UTC (42 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。