论文标题
在非紧凑空间中压力的不同
Differentiability of the pressure in non-compact spaces
论文作者
论文摘要
压力的规律性与相变有关。在本文中，我们研究了在非紧凑相位空间中定义的系统的热力学形式主义，我们的主要重点是可数的马尔可夫变化。我们产生了空间的度量压缩，使我们能够证明在残留集合和在均匀连续函数空间中的Aronszajn null集合外面的压力是可区分的。我们建立了一个标准，即所谓的扇形布置性能，这意味着原始系统和紧凑型中的压力重合。示例表明，紧凑型可以具有丰富的边界，例如提供康托尔集。
Regularity properties of the pressure are related to phase transitions. In this article we study thermodynamic formalism for systems defined in non-compact phase spaces, our main focus being countable Markov shifts. We produce metric compactifications of the space which allow us to prove that the pressure is differentiable on a residual set and outside an Aronszajn null set in the space of uniformly continuous functions. We establish a criterion, the so called sectorially arranged property, which implies that the pressure in the original system and in the compactification coincide. Examples showing that the compactifications can have rich boundaries, for example a Cantor set, are provided.
