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Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 2, Pages 23–27 (Mi faa2899)  

This article is cited in 3 scientific papers (total in 3 papers)

Topology of Real Algebraic Curves

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The problem on the existence of an additional first integral of the equations of geodesics on noncompact algebraic surfaces is considered. This problem was discussed as early as by Riemann and Darboux. We indicate coarse obstructions to integrability, which are related to the topology of the real algebraic curve obtained as the line of intersection of such a surface with a sphere of large radius. Some yet unsolved problems are discussed.

Keywords: geodesic flow, analytic first integral, geodesic convexity, $M$-curve

DOI: https://doi.org/10.4213/faa2899

Full text: PDF file (115 kB)
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English version:
Functional Analysis and Its Applications, 2008, 42:2, 98–102

Bibliographic databases:

UDC: 517.93+512.77
Received: 12.12.2007

Citation: V. V. Kozlov, “Topology of Real Algebraic Curves”, Funktsional. Anal. i Prilozhen., 42:2 (2008), 23–27; Funct. Anal. Appl., 42:2 (2008), 98–102

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Borisov A.V., Kilin A.A., Mamaev I.S., “The Hamiltonian dynamics of self-gravitating liquid and gas ellipsoids”, Regul. Chaotic Dyn., 14:2 (2009), 179–217  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Waters T.J., “Non-integrability of geodesic flow on certain algebraic surfaces”, Phys. Lett. A, 376:17 (2012), 1442–1445  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Borisov A. Mamaev I., “Rigid Body Dynamics”, Rigid Body Dynamics, de Gruyter Studies in Mathematical Physics, 52, Walter de Gruyter Gmbh, 2019, 1–520  mathscinet  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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