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
2023-08-29T08:15:11Z
dc.date.accessioned
2024-09-19T14:35:47Z
dc.date.available
2023-08-29T08:15:11Z
dc.date.available
2024-09-19T14:35:47Z
dc.date.issued
2023-07-01
dc.identifier.uri
http://hdl.handle.net/2072/536857
dc.description.abstract
In this short note, we prove that singular Reeb vector fields associated with generic b -contact forms on three dimensional manifolds with compact embedded critical surfaces have either (at least) 2N or an infinite number of escape orbits, where N denotes the number of connected components of the critical set. In case where the first Betti number of a connected component of the critical surface is positive, there exist infinitely many escape orbits. A similar result holds in the case of b -Beltrami vector fields that are not b -Reeb. The proof is based on a more detailed analysis of the main result in [19]. © 2023, Pleiades Publishing, Ltd.
eng
dc.description.sponsorship
Josep Fontana-McNally was supported by an INIREC grant of introduction to research financed under the project “Computational, Dynamical and Geometrical Complexity in Fluid Dynamics”, Ayudas Fundación BBVA a Proyectos de Investigación Científica 2021. Josep Fontana, Eva Miranda and Cédric Oms are partially supported by the Spanish State Research Agency grant PID2019-103849GB-I00 of AEI / 10.13039/501100011033 and 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 María 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 Fundación BBVA a Proyectos de Investigación Científica 2021. Cédric Oms acknowledges financial support from the Margarita Salas postdoctoral contract financed by the European Union-NextGenerationEU and is partially supported by the ANR grant “Cosy” (ANR-21-CE40-0002), partially supported by the ANR grant “CoSyDy” (ANR-CE40-0014). Daniel Peralta-Salas is supported by the grants CEX2019-000904-S, RED2022-134301-T and PID2019-106715GB GB-C21 funded by MCIN/AEI/10.13039/501100011033.
dc.format.extent
16 p.
cat
dc.publisher
Pleiades Publishing
cat
dc.relation.ispartof
Regular and Chaotic Dynamics
cat
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Beltrami vector fields; celestial mechanics; contact geometry; escape orbits
cat
dc.title
From 2N to Infinitely Many Escape Orbits
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/acceptedVersion
cat
dc.identifier.doi
10.1134/S1560354723520039
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
