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Regular and Chaotic Dynamics, 2018, Volume 23, Issue 3, Pages 304–324
DOI: https://doi.org/10.1134/S1560354718030061
(Mi rcd325)
 

This article is cited in 2 scientific papers (total in 2 papers)

On a Convex Embedding of the Euler Problem of Two Fixed Centers

Seongchan Kim

Mathematisches Institut, Universität Augsburg, Universitätsstrasse 14, Augsburg, 86159 Germany
Citations (2)
References:
Abstract: In this article, we study a convex embedding for the Euler problem of two fixed centers for energies below the critical energy level. We prove that the doubly-covered elliptic coordinates provide a 2-to-1 symplectic embedding such that the image of the bounded component near the lighter primary of the regularized Euler problem is convex for any energy below the critical Jacobi energy. This holds true if the two primaries have equal mass, but does not hold near the heavier body.
Keywords: convex embedding, global surface of section, Euler problem of two fixed centers.
Funding agency Grant number
Deutsche Forschungsgemeinschaft CI 45/8-1
FR 2637/2-1
This work is supported by DFG grants CI 45/8-1 and FR 2637/2-1.
Received: 16.10.2017
Accepted: 31.01.2018
Bibliographic databases:
Document Type: Article
MSC: 70F05, 35J35, 37J05
Language: English
Citation: Seongchan Kim, “On a Convex Embedding of the Euler Problem of Two Fixed Centers”, Regul. Chaotic Dyn., 23:3 (2018), 304–324
Citation in format AMSBIB
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\by Seongchan Kim
\paper On a Convex Embedding of the Euler Problem of Two Fixed Centers
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 3
\pages 304--324
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\crossref{https://doi.org/10.1134/S1560354718030061}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048098131}
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  • https://www.mathnet.ru/eng/rcd325
  • https://www.mathnet.ru/eng/rcd/v23/i3/p304
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:135
    References:23
     
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