Abstract:
This is the final paper in a series devoted to generic singularities
of geodesic flows for two-dimensional pseudo-Riemannian metrics of changing
signature and metrics induced from the Euclidean metric of the ambient space
on surfaces with a cuspidal edge. We study the local phase portraits
and the properties of geodesics at degenerate points of a certain type.
This completes the list of singularities in codimensions 1 and 2.
Keywords:
pseudo-Riemannian metric, geodesic, singular point, normal form, invariant manifold.
This paper was written with the financial support
of RFBR (grants no. 16-01-00766, no. 17-01-00849). Section 4
was written by the first author with the support of the Russian Science
Foundation (grant no. 17-11-01168).
Citation:
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
\Bibitem{PavRem19}
\by N.~G.~Pavlova, A.~O.~Remizov
\paper Completion of the classification of generic singularities of geodesic
flows in two classes of metrics
\jour Izv. Math.
\yr 2019
\vol 83
\issue 1
\pages 104--123
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Linking options:
https://www.mathnet.ru/eng/im8723
https://doi.org/10.1070/IM8723
https://www.mathnet.ru/eng/im/v83/i1/p119
This publication is cited in the following 5 articles:
Masatomo Takahashi, “On geodesics of framed surfaces in the Euclidean 3-space”, Tohoku Math. J. (2), 76:2 (2024)
A. O. Remizov, “Singulyarnosti kvazilineinykh differentsialnykh uravnenii”, Dalnevost. matem. zhurn., 23:1 (2023), 85–105
N. D. Pazij, N. G. Pavlova, “Local analytic classification for quasi-linear implicit differential systems at transversal singular points”, J. Dyn. Control Syst., 28:3 (2022), 453–464
N. G. Pavlova, A. O. Remizov, “Hyperbolic Roussarie fields with degenerate quadratic part”, Russian Math. Surveys, 76:2 (2021), 366–368
N. G. Pavlova, A. O. Remizov, “Smooth local normal forms of hyperbolic Roussarie vector fields”, Mosc. Math. J., 21:2 (2021), 413–426
Citation in format AMSBIB
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