标题： 关于无限梯子曲面上的一类类似伪Anosov的映射 显示英文标题

标题： On a family of pseudo-Anosov-like maps on the infinite ladder surface

摘要： 设$S_g$为亏格为$g$的闭曲面，$\mathcal{L}$为无限的雅各梯形曲面，$\mathrm{Map}(S)$表示曲面$S$的映射类群。设$q_g:\mathcal{L}\to S_g$为具有提升变换群$\mathbb{Z}$的正则无限叶覆盖。 在本文中，我们展示了在$\mathcal{L}$上存在“伪Anosov类似”的映射，这些映射是作为在$S_g$上Penner型伪Anosov映射在覆盖空间$q_g$下的提升而出现的。 此外，我们证明了这些提升是拓扑遍历的、混合的，并且支持零常返动力学。 此外，我们在$\mathcal{L}$上给出了这类映射的无限族的具体例子。 显示英文摘要

摘要： Let $S_g$ be the closed surface of genus $g$, $\mathcal{L}$ be the infinite Jacob's ladder surface, and $\mathrm{Map}(S)$ denote the mapping class group of a surface $S$. Let $q_g:\mathcal{L}\to S_g$ be the regular infinite-sheeted cover with deck transformation group $\mathbb{Z}$. In this paper, we show the existence of ``pseudo-Anosov-like'' maps on $\mathcal{L}$ that arise as the lifts of Penner-type pseudo-Anosov maps on $S_g$ under the cover $q_g$. Furthermore, we establish that these lifts are topologically transitive, mixing, and support null recurrent dynamics. Moreover, we present concrete examples of infinite families of such maps on $\mathcal{L}$.