Induced topological pressure for countable state Markov shifts
Induced topological pressure for countable state Markov shifts
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DOI：
10.1142/s0219493713500160
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发表时间：
2010-10
影响因子：
1.1
通讯作者：
Johannes Jaerisch;Marc Kessebohmer;Sanaz Lamei
中科院分区：
文献类型：
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作者：
Johannes Jaerisch;Marc Kessebohmer;Sanaz Lamei
我们推广了Savchenko的定义的拓扑熵的特殊流量可数马尔可夫移位考虑相应的概念的拓扑压力。对于一个大类的保持器连续的高度函数不一定有界远离零，这种压力可以表示为我们的新概念的诱导拓扑压力的可数状态马尔可夫位移关于一个非负的尺度函数和有限字的任意子集，我们能够建立一个变分原理在这种情况下。调查的依赖性的诱导压力的子集的话，我们给有趣的新结果连接Gurevic和经典的压力与耗尽原则的一大类马尔可夫移位。在这种情况下，我们考虑动态群扩展，以证明我们的新方法提供了一个有用的工具，底层组结构的可扩展性。
We generalise Savchenko's definition of topological entropy for special flows over countable Markov shifts by considering the corresponding notion of topological pressure. For a large class of Holder continuous height functions not necessarily bounded away from zero, this pressure can be expressed by our new notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words, and we are able to set up a variational principle in this context. Investigating the dependence of induced pressure on the subset of words, we give interesting new results connecting the Gurevic and the classical pressure with exhaustion principles for a large class of Markov shifts. In this context we consider dynamical group extensions to demonstrate that our new approach provides a useful tool to characterise amenability of the underlying group structure.