Geodesic
Singularities of a~geodesic flow on surfaces with a~cuspidal edge
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. I, Tome 268 (2010), pp. 258-267.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TM_2010_268_a16,
     author = {A. O. Remizov},
     title = {Singularities of a~geodesic flow on surfaces with a~cuspidal edge},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {258--267},
     publisher = {mathdoc},
     volume = {268},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_268_a16/}
}
TY  - JOUR
AU  - A. O. Remizov
TI  - Singularities of a~geodesic flow on surfaces with a~cuspidal edge
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2010
SP  - 258
EP  - 267
VL  - 268
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2010_268_a16/
LA  - ru
ID  - TM_2010_268_a16
ER  - 
%0 Journal Article
%A A. O. Remizov
%T Singularities of a~geodesic flow on surfaces with a~cuspidal edge
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2010
%P 258-267
%V 268
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2010_268_a16/
%G ru
%F TM_2010_268_a16
A. O. Remizov. Singularities of a~geodesic flow on surfaces with a~cuspidal edge. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. I, Tome 268 (2010), pp. 258-267. http://geodesic.mathdoc.fr/item/TM_2010_268_a16/

[1] Arnold V. I., Osobennosti kaustik i volnovykh frontov, Fazis, M., 1996 | MR | Zbl

[2] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii, MTsNMO, M., 2004

[3] Amores A. M., “A solution theorem for implicit differential equations. Applications to parallelism and geodesics for singular metrics”, Contribuciones matematicas: homenaje al profesor Enrique Outerelo Dominguez, Homen. Univ. Complut., Ed. Complut., Madrid, 2004, 1–12 | MR

[4] Kossowski M., Kriele M., “Signature type change and absolute time in general relativity”, Class. and Quantum Grav., 10 (1993), 1157–1164 | DOI | MR | Zbl

[5] Remizov A. O., “Geodezicheskie na dvumernykh poverkhnostyakh s psevdorimanovoi metrikoi: osobennosti smeny signatury”, Mat. sb., 200:3 (2009), 75–94 | DOI | MR | Zbl

[6] Roussarie R., Modèles locaux de champs et de formes, Astérisque, 30, Soc. math. France, Paris, 1975 | MR

[7] Remizov A. O., “Mnogomernaya konstruktsiya Puankare i osobennosti podnyatykh polei dlya neyavnykh differentsialnykh uravnenii”, Sovr. matematika. Fund. napr., 19, 2006, 131–170 | MR

[8] Bruce J. W., Fidal D. L., “On binary differential equations and umbilics”, Proc. Roy. Soc. Edinburgh A, 111 (1989), 147–168 | DOI | MR | Zbl

[9] Bruce J. W., Tari F., “On binary differential equations”, Nonlinearity, 8 (1995), 255–271 | DOI | MR | Zbl

[10] Samovol V. S., “Ekvivalentnost sistem differentsialnykh uravnenii v okrestnosti osoboi tochki”, Tr. Mosk. mat. o-va, 44, 1982, 213–234 | MR | Zbl

[11] Voronin S. M., “The Darboux–Whitney theorem and related questions”, Nonlinear Stokes phenomena, Adv. Sov. Math., 14, ed. Yu. S. Il'yashenko, Amer. Math. Soc., Providence, RI, 1993, 139–233 | MR | Zbl

[12] Voronin S. M., “Analiticheskaya klassifikatsiya rostkov golomorfnykh otobrazhenii s neizolirovannymi nepodvizhnymi tochkami i postoyannymi multiplikatorami i ee prilozheniya”, Vestn. Chelyabin. un-ta. Cer. 3, 1999, no. 2, 12–30 | MR

[13] Bryuno A. D., Lokalnyi metod nelineinogo analiza differentsialnykh uravnenii, Nauka, M., 1979 | MR

[14] Bryuno A. D., Stepennaya geometriya v algebraicheskikh i differentsialnykh uravneniyakh, Fizmatlit, M., 1998 | MR | Zbl