A comparison of categorical and topological entropies on Weinstein manifolds

Abstract

Let $W$ be a symplectic manifold, and let $\varphi :W\to W$ be a symplectic automorphism. Then, $\varphi$ induces an auto-equivalence $\Phi$ defined on the Fukaya category of $W$. In this paper, we prove that the categorical entropy of $\Phi$ bounds the topological entropy of $\varphi$ from below where $W$ is a Weinstein manifold and $\varphi$ is compactly supported. Moreover, being motivated by the work of Cineli, Ginzburg, and Gurel, we propose a conjecture which generalizes a result in dynamical system.

arXiv comment26 pages, 1 figure. The main change from the first version is that we provided more examples of symplectic automorphisms whose categorical entropy forces them to have positive topological entropy

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