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Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 1, Pages 119–139 (Mi izv8723)  

Completion of the classification of generic singularities of geodesic flows in two classes of metrics

N. G. Pavlovaab, A. O. Remizovcb

a Peoples Friendship University of Russia, Moscow
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
c CMAP École Polytechnique, Palaiseau, France

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00766
17-01-00849
Russian Science Foundation 17-11-01168
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).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/im8723

Full text: PDF file (784 kB)
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English version:
Izvestiya: Mathematics, 2019, 83:1, 104–123

Bibliographic databases:

UDC: 514.774.8+517.9
MSC: 53C22, 53B30, 34C05
Received: 26.09.2017
Revised: 20.06.2018

Citation: N. G. Pavlova, A. O. Remizov, “Completion of the classification of generic singularities of geodesic flows in two classes of metrics”, Izv. RAN. Ser. Mat., 83:1 (2019), 119–139; Izv. Math., 83:1 (2019), 104–123

Citation in format AMSBIB
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