论文标题
复合符号dehn曲折的动力学
Dynamics of composite symplectic Dehn twists
论文作者
论文摘要
本文似乎是双曲动力学，符号拓扑和低维拓扑的融合。我们表明，综合象征性的dehn Twist具有某些形式的不均匀双曲线：它具有积极的拓扑熵以及两个局部稳定和不稳定的lagrangian的家族，这些家族类似于Pseudo anosov ansosov ansosov ansosov mapping signatures。此外，我们表明，在迭代术下，这些组合的浮子共同体学组的排名呈指数增长，这部分回答了史密斯关于在较高维度中对符号映射类组的分类的问题。最后，我们提出了对模型的正熵熵的猜想，并指出了它与标准图的关系。
This paper appears as the confluence of hyperbolic dynamics, symplectic topology and low dimensional topology, etc. We show that composite symplectic Dehn twists have certain form of nonuniform hyperbolicity: it has positive topological entropy as well as two families of local stable and unstable Lagrangian manifolds, which are analogous to signatures of pseudo Anosov mapping classes. Moreover, we show that the rank of the Floer cohomology group of these compositions grows exponentially under iterations, which partially answers a question of Smith concerning the classification of symplectic mapping class group in higher dimensions. Finally, we propose a conjecture on the positive metric entropy of our model and point out its relationship with the standard map.
