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Regular and Chaotic Dynamics, 2003, Volume 8, Issue 4, Pages 413–430
DOI: https://doi.org/10.1070/RD2003v008n04ABEH000254 (Mi rcd792) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Non-integrability of restricted two body problems in constant curvature spaces

A. J. Maciejewskia, M. Przybylskabc

a Institute of Astronomy, University of Zielona Góra, Podgórna 50, PL-65–246 Zielona Góra, Poland
b INRIA, Projet Café, 2004, Route des Lucioles, B. P. 93, 06902 Sophia Antipolis Cedex, France
c Toruń Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87–100 Toruń, Poland
Citations (10)
DOI: https://doi.org/10.1070/RD2003v008n04ABEH000254
Abstract: We consider a restricted problem of two bodies in constant curvature spaces. The Newton and Hooke interactions between bodies are considered. For both types of interactions, we prove the non-integrability of this problem in spaces with constant non-zero curvature. Our proof is based on the Morales–Ramis theory.
Received: 18.11.2003
Bibliographic databases:
Document Type: Article
MSC: 37J30, 70H07, 34M35
Language: English
Citation: A. J. Maciejewski, M. Przybylska, “Non-integrability of restricted two body problems in constant curvature spaces”, Regul. Chaotic Dyn., 8:4 (2003), 413–430
Citation in format AMSBIB
\Bibitem{MacPrz03}
\by A. J. Maciejewski, M.~Przybylska
\paper Non-integrability of restricted two body problems in constant curvature spaces
\jour Regul. Chaotic Dyn.
\yr 2003
\vol 8
\issue 4
\pages 413--430
\mathnet{http://mi.mathnet.ru/rcd792}
\crossref{https://doi.org/10.1070/RD2003v008n04ABEH000254}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2023045}
\zmath{https://zbmath.org/?q=an:1048.37052}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2003RCD.....8..413M}
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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