无穷远处的压力与大偏差
Pressure at infinity and Large Deviations
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中文总结 AI 辅助
本文为可数马尔可夫移位上的连续时间悬停流建立第一级大偏差原理，引入无穷远处拓扑压力并证明变分原理，从而量化轨道逃逸至无穷远处的偏差，并展示紧支撑遍历测度的压力稠密性。
中文摘要 AI 辅助
我们为可数马尔可夫移位上的连续时间悬停流建立了第一级大偏差原理，这是一类非紧致动力系统。我们的结果既量化了伯克霍夫平均值偏离其典型值的偏差，更重要的是，为在有限时间内接近逃逸至无穷远处的轨道提供了大偏差原理。为克服非紧致性带来的挑战，我们引入了无穷远处拓扑压力的概念，并证明了一个变分原理，将其与测度论对应的概念联系起来。该框架允许研究一类自然的势，称为强正回归势，这类势具有稳健的热力学性质。此外，我们证明在此设定下，紧支撑遍历测度是压力稠密的。文中还给出了压力间隙的应用和例子。
英文摘要
We establish level-1 large deviation principles for continuous time suspension flows over countable Markov shifts, a class of non compact dynamical systems. Our results both quantify deviations of Birkhoff averages from their typical values and, importantly, provide a large deviation principle for orbits that at a finite time are close to escaping to infinity. To overcome the challenges posed by non compactness, we introduce the notion of topological pressure at infinity and prove a variational principle linking it to its measure theoretic counterpart. This framework allows the study of a natural class of potentials, known as strongly positive recurrent, which exhibit robust thermodynamic properties. Moreover, we show that compactly supported ergodic measures are pressure dense in this setting. Applications to pressure gaps and examples are given.
发表机构
- Pontificia Universidad Católica de Chile (UC)（智利天主教 Pontificia Universidad Católica 大学）
- University of Bristol（布里斯托大学）
机构由 AI 辅助整理，请以论文原文为准。
