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Funktsional'nyi Analiz i ego Prilozheniya, 2008, Volume 42, Issue 2, Pages 23–27
DOI: https://doi.org/10.4213/faa2899 (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
Full-text PDF (115 kB) Citations (3)
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DOI: https://doi.org/10.4213/faa2899
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.
Received: 12.12.2007
English version:
Functional Analysis and Its Applications, 2008, Volume 42, Issue 2, Pages 98–102
DOI: https://doi.org/10.1007/s10688-008-0015-5
Bibliographic databases:
Document Type: Article
UDC: 517.93+512.77
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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