dc.contributor.author
Fontana-McNally, J.
dc.contributor.author
Miranda, E.
dc.contributor.author
Oms, C.
dc.contributor.author
Peralta-Salas, D.
dc.date.accessioned
2025-01-14T10:07:32Z
dc.date.available
2025-01-14T10:07:32Z
dc.date.issued
2024-12-01
dc.identifier.uri
http://hdl.handle.net/2072/480023
dc.description.abstract
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 alpha and omega- limits both lie on Z (a generalized singular periodic orbit). This is the content of the generalized Weinstein conjecture.
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dc.description.sponsorship
Josep Fontana-McNally was supported by an INIREC grant Introduction to research financed under the project Computational, dynamical and geometrical complexity in fluid dynamics, Ayudas Fundacion BBVA a Proyectos de Investigacion Cientifica 2021. Josep Fontana, Eva Miranda and Cedric Oms are partially supported by the Spanish State Research Agency grants reference PID2019-103849GB-I00 of AEI/10.13039/501100011033 and PID2023-146936NB-I00 funded by MICIU/AEI/10.13039/501100011033 and, by ERDF/EU. They are also partially supported by the AGAUR project 2021 SGR 00603.Eva Miranda is supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2021 and by the Alexander von Humboldt Foundation via a Friedrich Wilhelm Bessel Research Award. Eva Miranda is also supported by the Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in R&D (project CEX2020-001084-M) . Eva Miranda and Daniel Peralta-Salas acknowledge partial support from the grant Computational, dynamical and geometrical complexity in fluid dynamics Ayudas Fundacion BBVA a Proyectos de Investigacion Cientifica 2021 with reference number EIC21-1-72.Cedric Oms acknowledges financial support from the Juan de la Cierva post-doctoral grant (grant number FCJ2021-046811-I) . 4 Daniel Peralta-Salas is supported by the grants CEX2023-001347-S, RED2022-134301-T and PID2022-136795NB-I00 funded by MCIN/AEI/10.13039/501100011033.
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dc.format.extent
27 p.
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dc.relation.ispartof
Advances in Mathematics
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dc.rights
(c) 2024 The Author(s)
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dc.rights
Attribution-NonCommercial-NoDerivatives 4.0 International
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dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/
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dc.subject.other
Weinstein conjecture
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dc.subject.other
Escape orbits
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dc.subject.other
Singular periodic orbit
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dc.subject.other
Reeb vector field
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dc.subject.other
Generalized Weinstein conjecture
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b- contact manifold
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dc.title
A counterexample to the singular Weinstein conjecture
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/publishedVersion
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dc.identifier.doi
10.1016/j.aim.2024.109998
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
