A counterexample to the singular Weinstein conjecture
In this article, we study the dynamical properties of Reeb vector fields on b-contact manifolds. We show that in dimension 3, the number of so-called singular periodic orbits can be prescribed. These constructions illuminate some key properties of escape orbits and singular periodic orbits, which pl...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/379042 |
| Acceso en línea: | http://hdl.handle.net/10261/379042 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85208090553&doi=10.1016%2fj.aim.2024.109998&partnerID=40&md5=34dd5c97567c2e2de52b849a3043a65d |
| Access Level: | acceso abierto |
| Palabra clave: | b-contact manifold Escape orbits Generalized Weinstein conjecture Reeb vector field Singular periodic orbit Weinstein conjecture |
| Sumario: | In this article, we study the dynamical properties of Reeb vector fields on b-contact manifolds. We show that in dimension 3, the number of so-called singular periodic orbits can be prescribed. These constructions illuminate some key properties of escape orbits and singular periodic orbits, which play a central role in formulating singular counterparts to the Weinstein conjecture and the Hamiltonian Seifert conjecture. In fact, we prove that the above-mentioned constructions lead to counterexamples of these conjectures as stated in [20]. Our construction shows that there are b-contact manifolds with no singular periodic orbits and no regular periodic orbits away from Z. We do not know whether there are constructions with no generalized escape orbits whose α and ω-limits both lie on Z (a generalized singular periodic orbit). This is the content of the generalized Weinstein conjecture. © 2024 The Authors |
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