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arXiv · 2208.13041

Dynamics of composite symplectic Dehn twists

Wenmin Gong·Zhijing Wendy Wang·Jinxin Xue
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Abstract

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, and provide a classification of the symplectic mapping class group of the $A^2_m$ configuration, 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.

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BibTeXRIS

Wenmin Gong, Zhijing Wendy Wang, Jinxin Xue. 2022-08-27. Dynamics of composite symplectic Dehn twists. https://doi.org/10.1007/s11425-025-2596-x

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