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Regular and Chaotic Dynamics, 2023, Volume 28, Issue 4-5, Pages 498–511
DOI: https://doi.org/10.1134/S1560354723520039 (Mi rcd1217) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Special Issue: On the 80th birthday of professor A. Chenciner

From $2N$ to Infinitely Many Escape Orbits

Josep Fontana-McNallya, Eva Mirandabc, Cédric Omsd, Daniel Peralta-Salase

a Laboratory of Geometry and Dynamical Systems, Universitat Politècnica de Catalunya, EPSEB-UPC, Av. Dr. Marañón, 44-50, 08028 Barcelona, Spain
b Centre de Recerca Matemàtica, CRM, Campus de Bellaterra, Edifici C, 08193 Barcelona, Spain
c Laboratory of Geometry and Dynamical Systems, Universitat Politècnica de Catalunya & IMtech, EPSEB-UPC, Av. Dr. Marañón, 44-50, 08028 Barcelona, Spain
d BCAM Basque Center of Applied Mathematics, Mazarredo Zumarkalea, 14, 48009 Bilbo, Bizkaia
e ICMAT, C. Nicolás Cabrera, 13-15, 28049 Madrid, Spain
Citations (3)
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DOI: https://doi.org/10.1134/S1560354723520039
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].
Keywords: contact geometry, Beltrami vector fields, escape orbits, celestial mechanics.
Funding agency Grant number
Agencia Estatal de Investigacion 10.13039/501100011033
0.13039/501100011033
Agència de Gestiö d'Ajuts Universitaris i de Recerca SGR 00603
Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D CEX2020-001084-M
CEX2019-000904-S
Agence Nationale de la Recherche ANR-21-CE40-0002
ANR-CE40- 0014
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.
Received: 30.03.2023
Accepted: 14.06.2023
Document Type: Article
MSC: 53D05, 53D17, 37N05
Language: English
Citation: Josep Fontana-McNally, Eva Miranda, Cédric Oms, Daniel Peralta-Salas, “From $2N$ to Infinitely Many Escape Orbits”, Regul. Chaotic Dyn., 28:4-5 (2023), 498–511
Citation in format AMSBIB
\Bibitem{FonMirOms23}
\by Josep Fontana-McNally, Eva Miranda, C\'edric Oms, Daniel Peralta-Salas
\paper From $2N$ to Infinitely Many Escape Orbits
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 4-5
\pages 498--511
\mathnet{http://mi.mathnet.ru/rcd1217}
\crossref{https://doi.org/10.1134/S1560354723520039}
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    Citing articles in Google Scholar: Russian citations, English citations
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