Positive topological entropy of positive contactomorphisms

IF 0.6 3区 数学 Q3 MATHEMATICS
Lucas Dahinden
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引用次数: 4

Abstract

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.
正接触形态的正拓扑熵
接触歧管的一种正接触态 $M$ 接触的终点是否开启 $M$ 它总是正横向于接触结构。假设 $M$ 包含一个Legendrian球 $\Lambda$,还有 $(M,\Lambda)$ 可以用刘维尔域填充吗 $(W,\omega)$ 精确拉格朗日量 $L$ 这样 $\omega|_{\pi_2(W,L)}=0$. 我们证明了如果作用的指数增长过滤包裹花的同调 $(W,L)$ 是正的,那么每一个正的接触形态的 $M$ 具有正的拓扑熵。该结果将Alves和Meiwes从Reeb流的结果推广到正接触形态,并给出了许多接触流形的例子,其中每个正接触形态都有正拓扑熵,其中包括Alves和Meiwes发现的奇异接触球。证明的一个主要步骤是证明包裹花同构与拉格朗日rabinowitz - flower同构的正部是同构的。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.
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