论文标题
部分可观测时空混沌系统的无模型预测
Topological entropy of pseudo-Anosov maps on punctured surfaces vs. homology of mapping tori
论文作者
论文摘要
我们研究了伪anosov图的拓扑熵在有刺穿的表面上的拓扑熵与其映射Tori的第一个同源性的等级。在表面上的$ s $ s $ s $ g $带有$ n $刺穿的属上，我们表明，伪 - anosov地图的熵从上面限制在$ \ dfrac {（k+1）\ log（k+3）} {|χ（q+3）} {| ub（ub ub（ub）|} | plostial $ k+k k+k+k+k+k+k+k+k+k+k+k+k+k+1 $ k+k+k+k+k+k+k+k+k+k+k+k+k+k+k+k+k+1 $ k+k+k+1这是对Tsai和Agol-Leininger-Margalit的先例作品的部分概括。
We investigate the relation between the topological entropy of pseudo-Anosov maps on surfaces with punctures and the rank of the first homology of their mapping tori. On the surface $S$ of genus $g$ with $n$ punctures, we show that the entropy of a pseudo-Anosov map is bounded from above by $\dfrac{(k+1)\log(k+3)}{|χ(S)|}$ up to a constant multiple when the rank of the first homology of the mapping torus is $k+1$ and $k, g, n$ satisfy a certain assumption. This is a partial generalization of precedent works of Tsai and Agol-Leininger-Margalit.
