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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.
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
Linking options:
https://www.mathnet.ru/eng/faa2899https://doi.org/10.4213/faa2899 https://www.mathnet.ru/eng/faa/v42/i2/p23
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Abstract page: | 930 | Full-text PDF : | 252 | References: | 102 | First page: | 35 |
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