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.
From: Wenmin Gong [view email]
[v1]
Sat, 27 Aug 2022 15:41:57 UTC (317 KB)
[v2]
Wed, 10 Jul 2024 02:35:08 UTC (326 KB)
[v3]
Wed, 17 Jun 2026 14:05:05 UTC (535 KB)
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