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Regular and Chaotic Dynamics, 2014, Volume 19, Issue 6, Pages 745–765
DOI: https://doi.org/10.1134/S1560354714060112
(Mi rcd196)
 

This article is cited in 14 scientific papers (total in 14 papers)

Invariant Manifolds at Infinity of the RTBP and the Boundaries of Bounded Motion

Regina Martíneza, Carles Simób

a Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona, Spain
b Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Catalunya, Spain
Citations (14)
References:
Abstract: Invariant manifolds of a periodic orbit at infinity in the planar circular RTBP are studied. To this end we consider the intersection of the manifolds with the passage through the barycentric pericenter. The intersections of the stable and unstable manifolds have a common even part, which can be seen as a displaced version of the two-body problem, and an odd part which gives rise to a splitting. The theoretical formulas obtained for a Jacobi constant C large enough are compared to direct numerical computations showing improved agreement when C increases. A return map to the pericenter passage is derived, and using an approximation by standard-like maps, one can make a prediction of the location of the boundaries of bounded motion. This result is compared to numerical estimates, again improving for increasing C. Several anomalous phenomena are described.
Keywords: invariant rotational curves, separatrix maps, splitting function, restricted three-body problem.
Funding agency Grant number
Ministerio de Economía y Competitividad de España MTM2010-16425
MTM2013-41168
Generalitat de Catalunya 2009 SGR 67
2014 SGR 1145
This work has been supported by grants MTM2010-16425 and MTM2013-41168 (Spain), 2009 SGR 67 and 2014 SGR 1145 (Catalonia).
Received: 20.10.2014
Accepted: 06.11.2014
Bibliographic databases:
Document Type: Article
MSC: 37N05, 70F07, 37E99
Language: English
Citation: Regina Martínez, Carles Simó, “Invariant Manifolds at Infinity of the RTBP and the Boundaries of Bounded Motion”, Regul. Chaotic Dyn., 19:6 (2014), 745–765
Citation in format AMSBIB
\Bibitem{MarSim14}
\by Regina Mart{\'\i}nez, Carles Sim\'o
\paper Invariant Manifolds at Infinity of the RTBP and the Boundaries of Bounded Motion
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 6
\pages 745--765
\mathnet{http://mi.mathnet.ru/rcd196}
\crossref{https://doi.org/10.1134/S1560354714060112}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3284613}
\zmath{https://zbmath.org/?q=an:06507831}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000345996200011}
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  • https://www.mathnet.ru/eng/rcd/v19/i6/p745
  • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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