A Bangert–Hingston theorem for starshaped hypersurfaces

IF 0.7 1区数学 Q2 MATHEMATICS

Journal of Modern Dynamics Pub Date : 2022-04-13 DOI:10.3934/jmd.2023011

Alessio Pellegrini

引用次数: 0

Abstract

Let $Q$ be a closed manifold with non-trivial first Betti number that admits a non-trivial $S^1$-action, and $\Sigma \subseteq T^*Q$ a non-degenerate starshaped hypersurface. We prove that the number of geometrically distinct Reeb orbits of period at most $T$ on $\Sigma$ grows at least logarithmically in $T$.

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星形超曲面的Bangert-Hingston定理

设$Q$是一个具有非平凡第一Betti数的闭流形，它承认一个非平凡的$S^1$-作用，$\Sigma \子集$ T^*Q$是一个非简并星形超曲面。我们证明了在$ $ $\Sigma$上周期不超过$ $T$的几何上不同的Reeb轨道的数目在$ $ $T$中至少呈对数增长。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Modern Dynamics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Modern Dynamics (JMD) is dedicated to publishing research articles in active and promising areas in the theory of dynamical systems with particular emphasis on the mutual interaction between dynamics and other major areas of mathematical research, including: Number theory Symplectic geometry Differential geometry Rigidity Quantum chaos Teichmüller theory Geometric group theory Harmonic analysis on manifolds. The journal is published by the American Institute of Mathematical Sciences (AIMS) with the support of the Anatole Katok Center for Dynamical Systems and Geometry at the Pennsylvania State University.