Besse和Zoll Reeb流的谱特征

IF 1.8 1区数学 Q1 MATHEMATICS, APPLIED

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-05-01 DOI:10.1016/j.anihpc.2020.08.004

Viktor L. Ginzburg , Başak Z. Gürel , Marco Mazzucchelli

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引用次数: 9

摘要

当一个闭合接触流形的所有Reeb轨道都闭合时，它被称为Besse，当它们具有相同的最小周期时，它被称为Zoll。本文用s1等变谱不变量给出了凸接触球和黎曼单位切线束的贝塞接触形式的表征。此外，对于辛向量空间的受限接触型超曲面，我们通过Ekeland-Hofer能力给出了Besse性质的充分条件。

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On the spectral characterization of Besse and Zoll Reeb flows

A closed contact manifold is called Besse when all its Reeb orbits are closed, and Zoll when they have the same minimal period. In this paper, we provide a characterization of Besse contact forms for convex contact spheres and Riemannian unit tangent bundles in terms of $S^{1}$ -equivariant spectral invariants. Furthermore, for restricted contact type hypersurfaces of symplectic vector spaces, we give a sufficient condition for the Besse property via the Ekeland–Hofer capacities.

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来源期刊

Annales De L Institut Henri Poincare-Analyse Non Lineaire 数学-应用数学

CiteScore

4.10

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.