论文标题
转移操作员的准紧凑型拓扑马尔可夫的转移带有孔
Quasi-compactness of transfer operators for topological Markov shifts with holes
论文作者
论文摘要
我们考虑具有可数州的拓扑马尔可夫班次（TMS）的转移运营商，孔为$ 2 $ - 圆柱形。作为主要结果，如果换档的封闭系统具有有限的不可还原过渡矩阵，并且电势是较弱的Lipschitz连续且可总结的，那么我们获得了相关Ruelle转移操作员的Ruelle-Perron-Perron-Frobenius Theorem和Quasi-Compactness。还计算了开放系统的逃逸率。在推论中，事实证明，在拓扑上的TMS上具有可总结潜力的Ruelle操作员具有光谱间隙属性。作为其他示例，我们将主要结果应用于与图形迭代函数系统相关的传输运算符。
We consider transfer operators for topological Markov shift (TMS) with countable states and with holes which are $2$-cylinders. As main results, if the closed system of the shift has finitely irreducible transition matrix and the potential is a weaker Lipschitz continuous and summable, then we obtain a version of Ruelle-Perron-Frobenius Theorem and quasi-compactness of the associated Ruelle transfer operator. The escape rate of the open system is also calculated. In corollary, it turns out that the Ruelle operator of summable potential on topologically transitive TMS has a spectral gap property. As other example, we apply the main results to the transfer operators associated to graph iterated function systems.
