Pressure and equilibrium states for countable state markov shifts

Doris Fiebig; Ulf-Rainer Fiebig; Michiko Yuri

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Pressure and equilibrium states for countable state markov shifts

机译：可数状态马尔可夫位移的压力和平衡状态

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We give a general definition of the topological pressureP top (f, S) for continuous real valued functionsf: X→ℝ on transitive countable state Markov shifts (X, S). A variational principle holds for functions satisfying a mild distortion property. We introduce a new notion of Z-recurrent functions. Given any such functionf, we show a general method how to obtain tight sequences of invariant probability measures supported on periodic points such that a weak accumulation pointμ is an equilibrium state forf if and only if εf − dμ<∞. We discuss some conditions that ensure this integrability. As an application we obtain the Gauss measure as a weak limit of measures supported on periodic points.

机译：我们给出了连续实值函数f的拓扑压力P top （f，S）的一般定义：传递可数状态Markov位移（X，S）的X→ℝ。变分原理适用于满足轻微失真特性的功能。我们介绍了Z递归函数的新概念。给定任何这样的函数，我们将展示一种通用方法，该方法如何获取在周期点上支持的不变概率测度的紧序列，以使得弱累积点μ在且仅当εf-dμ<∞时才是平衡状态。我们讨论了确保这种可集成性的一些条件。作为应用，我们获得高斯测度作为周期点支持的测度的弱极限。

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《Israel Journal of Mathematics》 |2002年第1期|221-257|共37页
作者
Doris Fiebig; Ulf-Rainer Fiebig; Michiko Yuri;
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Institut für Mathematische Stochastik Universität Göttingen;

Institut für Angewandte Mathematik Universität Heidelberg;

Department of Business Administration Sapporo University Nishioka;

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Pressure and equilibrium states for countable state markov shifts

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