驯服图上映射的常斜率、熵和马蹄形
Constant slope, entropy and horseshoes for a map on a tame graph
摘要：
我们研究定义在驯服图上的连续可数（严格）单调映射，即，一种特殊的皮亚诺连续体，其包含分支点和端点的集合具有可数闭包。在我们的研究中，我们仅限于可数马尔可夫情形。本文给出了一个充要条件，在此条件下，一个驯服图$G$的一个局部最终到上的可数马尔可夫映射$f$与一个可数仿射驯服图的一个常斜率映射$g$共轭。特别地，我们证明了在马尔可夫映射$f$对应于递归转移阵的情况下，对于常斜率$e^{h_{\operatorname{top}}(f)}$，满足条件，其中$h_{\operatorname{top}}(f)$是$f$的拓扑熵.此外，我们表明，在我们的类的拓扑熵$h_{\operatorname{top}}(f)$是通过映射$f$的马蹄铁。
英文摘要：
We study continuous countably (strictly) monotone maps defined on a tame graph, i.e., a special Peano continuum for which the set containing branchpoints and endpoints has a countable closure. In our investigation we confine ourselves to the countable Markov case. We show a necessary and sufficient condition under which a locally eventually onto, countably Markov map $f$ of a tame graph $G$ is conjugate to a constant slope map $g$ of a countably affine tame graph. In particular, we show that in the case of a Markov map $f$ that corresponds to recurrent transition matrix, the condition is satisfied for constant slope $e^{h_{\operatorname{top}}(f)}$, where $h_{\operatorname{top}}(f)$ is the topological entropy of $f$. Moreover, we show that in our class the topological entropy $h_{\operatorname{top}}(f)$ is achievable through horseshoes of the map $f$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
