Dynamics of composite symplectic Dehn twists

Abstract: It is classically known in Nielson-Thurston theory that the mapping class group of a hyperbolic surface is generated by Dehn twists and most elements are pseudo Anosov. Pseudo Anosov elements are interesting dynamical objects. They are featured by positive topological entropy and two invariant singular foliations expanded or contracted by the dynamics. We explore a generalization of these ideas to symplectic mapping class groups. With the symplectic Dehn twists along Lagrangian spheres introduced by Arnold and Seidel, we show in various settings that the compositions of such twists has features of pseudo Anosov elements, such as positive topological entropy, invariant stable and unstable laminitions, exponential growth of Floer homology group, etc. This is a joint work with Wenmin Gong and Zhijing Wang.

differential geometrydynamical systemsgeometric topologysymplectic geometryspectral theory

Audience: researchers in the topic

Geometry and Dynamics seminar

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