论文标题
吉布斯状态的存在，并最大程度地提高了马尔可夫结构的一般一维晶格系统的措施
Existence of Gibbs states and maximizing measures on a general one-dimensional lattice system with markovian structure
论文作者
论文摘要
考虑一个紧凑的度量空间$（m，d_m）$和$ x = m^{\ mathbb {n}} $。我们证明了Ruelle的Perron Frobenius定理，用于[Bull中引入的Markovian结构。布拉斯。数学。 Soc。 45（2014），第53-72页，由连续函数$ a：m \ times m \ to \ mathbb {r} $定义，它决定了可允许序列的集合。特别是，这类子缩影包括有限的马尔可夫偏移和模型，其中单位圆$ s^1 $给出了字母。使用涉及内核，我们表征了与其最大特征值相关的ruelle操作员的归一化特征功能，并将其相应的吉布斯状态扩展到双边方法。从这些结果中，我们证明了在特定的可计数马尔可夫偏移类别中的平衡状态和零温度下的积累点的存在。
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.
