A positive contactomorphism of a contact manifold $M$ is the end point of a contact isotopy on $M$ that is always positively transverse to the contact structure. Assume that $M$ contains a Legendrian sphere $\Lambda$, and that $(M,\Lambda)$ is fillable by a Liouville domain $(W,\omega)$ with exact Lagrangian $L$ such that $\omega|_{\pi_2(W,L)}=0$. We show that if the exponential growth of the action filtered wrapped Floer homology of $(W,L)$ is positive, then every positive contactomorphism of $M$ has positive topological entropy. This result generalizes the result of Alves and Meiwes from Reeb flows to positive contactomorphisms, and it yields many examples of contact manifolds on which every positive contactomorphism has positive topological entropy, among them the exotic contact spheres found by Alves and Meiwes. A main step in the proof is to show that wrapped Floer homology is isomorphic to the positive part of Lagrangian Rabinowitz-Floer homology.

中文翻译：

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正接触同构的正拓扑熵

接触流形 $M$ 的正接触同构是 $M$ 上的接触同位素的端点，它总是正横向于接触结构。假设 $M$ 包含一个勒让德球 $\Lambda$，并且 $(M,\Lambda)$ 可以被具有精确拉格朗日 $L$ 的刘维尔域 $(W,\omega)$ 填充，使得 $\omega| _{\pi_2(W,L)}=0$。我们表明，如果 $(W,L)$ 的动作过滤包裹 Floer 同源性的指数增长是正的，那么 $M$ 的每个正接触同构都具有正拓扑熵。该结果将 Reeb 流的 Alves 和 Meiwes 的结果推广到正接触同胚，并产生了许多接触流形的例子，其中每个正接触同胚都具有正拓扑熵，其中包括 Alves 和 Meiwes 发现的奇异接触球。