RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Regul. Chaotic Dyn., 2014, Volume 19, Issue 6, Pages 601–606 (Mi rcd8)  

This article is cited in 9 scientific papers (total in 11 papers)

On Rational Integrals of Geodesic Flows

Valery V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: This paper is concerned with the problem of first integrals of the equations of geodesics on two-dimensional surfaces that are rational in the velocities (or momenta). The existence of nontrivial rational integrals with given values of the degrees of the numerator and the denominator is proved using the Cauchy–Kovalevskaya theorem.

Keywords: conformal coordinates, rational integral, irreducible integrals, Cauchy–Kovalevskaya theorem

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Scientific Foundation.


DOI: https://doi.org/10.1134/S156035471406001X

References: PDF file   HTML file

Bibliographic databases:

MSC: 34A34, 58E10
Received: 29.09.2014
Accepted:17.10.2014
Language:

Citation: Valery V. Kozlov, “On Rational Integrals of Geodesic Flows”, Regul. Chaotic Dyn., 19:6 (2014), 601–606

Citation in format AMSBIB
\Bibitem{Koz14}
\by Valery V. Kozlov
\paper On Rational Integrals of Geodesic Flows
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 6
\pages 601--606
\mathnet{http://mi.mathnet.ru/rcd8}
\crossref{https://doi.org/10.1134/S156035471406001X}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3284603}
\zmath{https://zbmath.org/?q=an:06507821}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2014RCD....19..601K}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000345996200001}


Linking options:
  • http://mi.mathnet.ru/eng/rcd8
  • http://mi.mathnet.ru/eng/rcd/v19/i6/p601

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Translation

    This publication is cited in the following articles:
    1. S. P. Kuznetsov, “On the validity of the nonholonomic model of the rattleback”, Phys. Usp., 58:12 (2015), 1223–1224  mathnet  crossref  crossref  adsnasa  isi  elib
    2. A. V. Borisov, I. S. Mamaev, “Zamechaniya o novykh modelyakh treniya i negolonomnoi mekhanike”, UFN, 185:12 (2015), 1339–1341  mathnet  crossref
    3. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Alain Albouy, “Projective Dynamics and First Integrals”, Regul. Chaotic Dyn., 20:3 (2015), 247–276  mathnet  crossref  mathscinet  zmath  adsnasa
    5. V. V. Kozlov, “Polynomial conservation laws for the Lorentz gas and the Boltzmann–Gibbs gas”, Russian Math. Surveys, 71:2 (2016), 253–290  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Valery V. Kozlov, “On the Extendability of Noether’s Integrals for Orbifolds of Constant Negative Curvature”, Regul. Chaotic Dyn., 21:7-8 (2016), 821–831  mathnet  crossref  mathscinet
    7. A. Aoki, T. Houri, K. Tomoda, “Rational first integrals of geodesic equations and generalised hidden symmetries”, Classical Quantum Gravity, 33:19 (2016), 195003, 12 pp.  crossref  mathscinet  zmath  isi  scopus
    8. B. Kruglikov, V. S. Matveev, “The geodesic flow of a generic metric does not admit nontrivial integrals polynomial in momenta”, Nonlinearity, 29:6 (2016), 1755–1768  crossref  mathscinet  zmath  isi  scopus
    9. M. V. Pavlov, S. P. Tsarev, “On local description of two-dimensional geodesic flows with a polynomial first integral”, J. Phys. A, 49:17 (2016), 175201, 20 pp.  crossref  mathscinet  zmath  isi  scopus
    10. Yu. Yu. Bagderina, “Ratsionalnye integraly vtoroi stepeni dvumernykh uravnenii geodezicheskikh”, Sib. elektron. matem. izv., 14 (2017), 33–40  mathnet  crossref
    11. N. V. Denisova, “Polynomial integrals of mechanical systems on a torus with a singular potential”, Dokl. Phys., 62:8 (2017), 397–399  crossref  mathscinet  isi  scopus
  • Number of views:
    This page:131
    References:30

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019