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Regular and Chaotic Dynamics, 2017, Volume 22, Issue 4, Pages 408–434
DOI: https://doi.org/10.1134/S1560354717040050 (Mi rcd263) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Periodic Orbits in the Restricted Three-body Problem and Arnold’s $J^+$-invariant

Kai Cieliebaka, Urs Frauenfeldera, Otto van Koertb

a Mathematisches Institut, Universität Augsburg, Universitätsstrasse 14, Augsburg, 86159 Germany
b Department of Mathematics and Research Institute of Mathematics, Seoul National University, San 56-1, Sillim-dong, Gwanak-gu, Seoul 08826, South Korea
Citations (9)
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DOI: https://doi.org/10.1134/S1560354717040050
Abstract: We apply Arnold’s theory of generic smooth plane curves to Stark–Zeeman systems. This is a class of Hamiltonian dynamical systems that describes the dynamics of an electron in an external electric and magnetic field, and includes many systems from celestial mechanics. Based on Arnold’s $J^+$-invariant, we introduce invariants of periodic orbits in planar Stark–Zeeman systems and study their behavior.
Keywords: generic immersions into the plane, Arnold’s plane curve invariants, restricted threebody problem.
Funding agency Grant number
Deutsche Forschungsgemeinschaft CI 45/8-1
FR 2637/2-1
National Research Foundation of Korea NRF-2016R1C1B2007662
K.C. was supported by DFG grant CI 45/8-1, U.F. by DFG grant FR 2637/2-1, and O.v.K. by NRF grant NRF-2016R1C1B2007662.
Received: 03.05.2017
Accepted: 26.06.2017
Bibliographic databases:
Document Type: Article
MSC: 53A04, 57R42, 70F05, 70F07, 05C10
Language: English
Citation: Kai Cieliebak, Urs Frauenfelder, Otto van Koert, “Periodic Orbits in the Restricted Three-body Problem and Arnold’s $J^+$-invariant”, Regul. Chaotic Dyn., 22:4 (2017), 408–434
Citation in format AMSBIB
\Bibitem{CieFraVan17}
\by Kai Cieliebak, Urs Frauenfelder, Otto van Koert
\paper Periodic Orbits in the Restricted Three-body Problem and Arnold’s $J^+$-invariant
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 4
\pages 408--434
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\crossref{https://doi.org/10.1134/S1560354717040050}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85026877239}
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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