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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 268, Pages 258–267 (Mi tm2868)  
This article is cited in 7 scientific papers (total in 7 papers)

Singularities of a geodesic flow on surfaces with a cuspidal edge

A. O. Remizov

International School for Advanced Studies (SISSA), Trieste, Italy
Full-text PDF (212 kB) Citations (7)
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Abstract: This paper is a study of singularities of geodesic flows on surfaces with nonisolated singular points that form a smooth curve (like a cuspidal edge). The main results of the paper are normal forms of the corresponding direction field on the tangent bundle of the plane of local coordinates and the projection of its trajectories to the surface.
Received in September 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 268, Pages 248–257
DOI: https://doi.org/10.1134/S0081543810010177
Bibliographic databases:
Document Type: Article
UDC: 514.774+517.974.8+517.922
Language: Russian
Citation: A. O. Remizov, “Singularities of a geodesic flow on surfaces with a cuspidal edge”, Differential equations and topology. I, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 268, MAIK Nauka/Interperiodica, Moscow, 2010, 258–267; Proc. Steklov Inst. Math., 268 (2010), 248–257
Citation in format AMSBIB
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\by A.~O.~Remizov
\paper Singularities of a~geodesic flow on surfaces with a~cuspidal edge
\inbook Differential equations and topology.~I
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2010
\vol 268
\pages 258--267
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm2868}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2010
\vol 268
\pages 248--257
\crossref{https://doi.org/10.1134/S0081543810010177}
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Linking options:
  • https://www.mathnet.ru/eng/tm2868
  • https://www.mathnet.ru/eng/tm/v268/p258
    • This publication is cited in the following 7 articles:
    1. Masatomo Takahashi, “On geodesics of framed surfaces in the Euclidean 3-space”, Tohoku Math. J. (2), 76:2 (2024)  crossref
    2. Honda A., Naokawa K., Umehara M., Yamada K., “Isometric Deformations of Wave Fronts At Non-Degenerate Singular Points”, Hiroshima Math. J., 50:3 (2020), 269–312  crossref  mathscinet  isi
    3. N. G. Pavlova, A. O. Remizov, “Completion of the classification of generic singularities of geodesic flows in two classes of metrics”, Izv. Math., 83:1 (2019), 104–123  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Ortiz-Bobadilla L., Rosales-Gonzalez E., Voronin S.M., “Analytic Classification of Foliations Induced By Germs of Holomorphic Vector Fields in (C-N,0) With Non-Isolated Singularities”, J. Dyn. Control Syst., 25:3 (2019), 491–516  crossref  mathscinet  isi
    5. M. A. Davydova, N. T. Levashova, S. A. Zakharova, “Asimptoticheskii analiz v zadache modelirovaniya protsessa perenosa gazovoi primesi v pripoverkhnostnom sloe atmosfery”, Model. i analiz inform. sistem, 23:3 (2016), 283–290  mathnet  crossref  mathscinet  elib
    6. Ghezzi R., Remizov A.O., “On a Class of Vector Fields with Discontinuities of Divide-by-Zero Type and its Applications to Geodesics in Singular Metrics”, J. Dyn. Control Syst., 18:1 (2012), 135–158  crossref  mathscinet  zmath  isi  scopus
    7. N. G. Pavlova, A. O. Remizov, “Geodesics on hypersurfaces in Minkowski space: singularities of signature change”, Russian Math. Surveys, 66:6 (2011), 1201–1203  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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