一般一维马氏结构格点系统的吉布斯态和极大化测度的存在性
Existence of Gibbs states and maximizing measures on a general one-dimensional lattice system with markovian structure
摘要：
考虑紧致度量空间$(M, d_M)$和$X = M^{\mathbb{N}}$ .本文证明了[Bull. Braz. Math.Soc.45（2014），pp. 53-72]，其从确定容许序列的集合的连续函数$A : M \times M \to \mathbb{R}$定义。特别地，这类子移位包括有限马尔可夫移位和其中字母表由单位圆$S^1$给出的模型。利用对合核，我们刻画了Ruelle算子的归一化本征函数及其最大本征值，并将其相应的吉布斯态推广到双边方法.从这些结果中，我们证明了一类特殊的可数马氏位移在零温下存在平衡态和聚点。
英文摘要：
Consider a compact metric space $(M, d_M)$ and $X = M^{\mathbb{N}}$. We prove a Ruelle's Perron Frobenius Theorem for a class of compact subshifts with Markovian structure introduced in [Bull. Braz. Math. Soc. 45 (2014), pp. 53-72] which are defined from a continuous function $A : M \times M \to \mathbb{R}$ that determines the set of admissible sequences. In particular, this class of subshifts includes the finite Markov shifts and models where the alphabet is given by the unit circle $S^1$. Using the involution Kernel, we characterize the normalized eigenfunction of the Ruelle operator associated to its maximal eigenvalue and present an extension of its corresponding Gibbs state to the bilateral approach. From these results, we prove existence of equilibrium states and accumulation points at zero temperature in a particular class of countable Markov shifts.
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