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Regular and Chaotic Dynamics, 2009, Volume 14, Issue 4-5, Pages 455–465
DOI: https://doi.org/10.1134/S1560354709040030 (Mi rcd975) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Proceedings of GDIS 2008, Belgrade

Isomorphisms of geodesic flows on quadrics

A. V. Borisov, I. S. Mamaev

Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
Citations (7)
DOI: https://doi.org/10.1134/S1560354709040030
Abstract: We consider several well-known isomorphisms between Jacobi’s geodesic problem and some integrable cases from rigid body dynamics (the cases of Clebsch and Brun). A relationship between these isomorphisms is indicated. The problem of compactification for geodesic flows on noncompact surfaces is stated. This problem is hypothesized to be intimately connected with the property of integrability.
Keywords: quadric, geodesic flows, integrability, compactification, regularization, isomorphism.
Received: 06.06.2008
Accepted: 02.03.2009
Bibliographic databases:
Document Type: Personalia
MSC: 53C22, 37Kxx
Language: English
Citation: A. V. Borisov, I. S. Mamaev, “Isomorphisms of geodesic flows on quadrics”, Regul. Chaotic Dyn., 14:4-5 (2009), 455–465
Citation in format AMSBIB
\Bibitem{BorMam09}
\by A. V. Borisov, I. S. Mamaev
\paper Isomorphisms of geodesic flows on quadrics
\jour Regul. Chaotic Dyn.
\yr 2009
\vol 14
\issue 4-5
\pages 455--465
\mathnet{http://mi.mathnet.ru/rcd975}
\crossref{https://doi.org/10.1134/S1560354709040030}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2551869}
\zmath{https://zbmath.org/?q=an:1229.37096}
Linking options:
  • https://www.mathnet.ru/eng/rcd975
  • https://www.mathnet.ru/eng/rcd/v14/i4/p455
    • This publication is cited in the following 7 articles:
    1. K. G. Shvarts, “Advective Flow of a Rotating Fluid Layer in a Vibrational Field”, Rus. J. Nonlin. Dyn., 15:3 (2019), 261–270  mathnet  crossref  mathscinet  elib
    2. Pantelis A. Damianou, “Poisson Brackets after Jacobi and Plücker”, Regul. Chaotic Dyn., 23:6 (2018), 720–734  mathnet  crossref
    3. Andrey V. Tsiganov, “Killing Tensors with Nonvanishing Haantjes Torsion and Integrable Systems”, Regul. Chaotic Dyn., 20:4 (2015), 463–475  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    4. Alain Albouy, Trends in Mathematics, 4, Extended Abstracts Spring 2014, 2015, 3  crossref
    5. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Superintegrable Generalizations of the Kepler and Hook Problems”, Regul. Chaotic Dyn., 19:3 (2014), 415–434  mathnet  crossref  mathscinet  zmath
    6. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “The Dynamics of Vortex Rings: Leapfrogging, Choreographies and the Stability Problem”, Regul. Chaotic Dyn., 18:1-2 (2013), 33–62  mathnet  crossref  mathscinet  zmath
    7. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Dinamika vikhrevykh kolets: chekharda, khoreografii i problema ustoichivosti”, Nelineinaya dinam., 8:1 (2012), 113–147  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
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