On the subsystems of topological Markov chains
On the subsystems of topological Markov chains
复制标题
关于拓扑马尔可夫链的子系统
DOI：
10.1017/s0143385700001516
复制
发表时间：
1982
影响因子：
0.9
通讯作者：
Wolfgang Krieger
中科院分区：
文献类型：
--
作者：
Wolfgang Krieger
设SA是一个不可约的非周期拓扑马尔可夫链。如果S_n是一个不可约非周期拓扑马尔可夫链，且其拓扑熵小于SA的拓扑熵，则存在一个不可约非周期拓扑马尔可夫链，其拓扑熵等于S_n处的拓扑熵，它是SA的一个子系统.若S是Cantor不连续统的扩张同胚，且S的拓扑熵小于SA的拓扑熵，且对任意j∈ N，S的最小周期j的周期点个数小于或等于SA的最小周期j的周期点个数，则S与SA的一个子系统拓扑共轭.
Abstract Let SA be an irreducible and aperiodic topological Markov chain. If SĀ is an irreducible and aperiodic topological Markov chain, whose topological entropy is less than that of SA, then there exists an irreducible and aperiodic topological Markov chain, whose topological entropy equals the topological entropy at SĀ, and that is a subsystem of SA. If S is an expansive homeomorphism of the Cantor discontinuum, whose topological entropy is less than that of SA, and such that for every j∈ℕ the number of periodic points of least period j of S is less than or equal to the number of periodic points of least period j of SA, then S is topological conjugate to a subsystem of SA.