悬浮流的重现性和瞬变性
Recurrence and transience for suspension flows
摘要：
我们研究了可数马尔可夫位移上的悬浮流的热力学形式，其屋顶函数不一定远离零。建立了正则势平衡测度存在唯一的条件。我们定义的概念，在这种情况下的潜在的复发和瞬态。我们定义的“更新流”，这是一个符号模型的一类具有不同的复发功能的流。我们研究了相应的热力学形式主义，建立了存在平衡测度和相变的条件。给出了定义在具有抛物不动点的区间映射上的悬浮流的应用。
英文摘要：
We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for regular potentials. We define the notions of recurrence and transience of a potential in this setting. We define the "renewal flow", which is a symbolic model for a class of flows with diverse recurrence features. We study the corresponding thermodynamic formalism, establishing conditions for the existence of equilibrium measures and phase transitions. Applications are given to suspension flows defined over interval maps having parabolic fixed points.
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