{"title":"星形超曲面的Bangert-Hingston定理","authors":"Alessio Pellegrini","doi":"10.3934/jmd.2023011","DOIUrl":null,"url":null,"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 $T$.","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Bangert–Hingston theorem for starshaped hypersurfaces\",\"authors\":\"Alessio Pellegrini\",\"doi\":\"10.3934/jmd.2023011\",\"DOIUrl\":null,\"url\":null,\"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 $T$.\",\"PeriodicalId\":51087,\"journal\":{\"name\":\"Journal of Modern Dynamics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-04-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Modern Dynamics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/jmd.2023011\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Modern Dynamics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/jmd.2023011","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Bangert–Hingston theorem for starshaped hypersurfaces
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 $T$.
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.
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