Geodesic
Investigation of a 3D system of differential equations with non-isolated
Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 3, pp. 332-337.

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

A system of the family, considered in the papers of A.O. Remizov, is investigated. For all the fields of the family, the origin is a non-isolated singular point of a complicated nature (the linear part of the field at the singular point can have the type "nilpotent Jordan cell" ). It was shown by A.O. Remizov (with coauthors) that for the considered vector fields there exists one-parametric family of the phase curves entering into the singular point; for a certain case there is also one additional phase curve with the same property. In the present paper we consider one of the vector fields of the Remizov family, apparently not studied previously. For this vector field analogous results to the pointed above are obtained.
Keywords: nonisolated singular point, degenerated singular point, blow-up. 
@article{CHFMJ_2018_3_3_a5,
     author = {E. A. Chirkova},
     title = {Investigation of a {3D} system of differential equations with non-isolated},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {332--337},
     publisher = {mathdoc},
     volume = {3},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a5/}
}
TY  - JOUR
AU  - E. A. Chirkova
TI  - Investigation of a 3D system of differential equations with non-isolated
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2018
SP  - 332
EP  - 337
VL  - 3
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a5/
LA  - ru
ID  - CHFMJ_2018_3_3_a5
ER  - 
%0 Journal Article
%A E. A. Chirkova
%T Investigation of a 3D system of differential equations with non-isolated
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2018
%P 332-337
%V 3
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a5/
%G ru
%F CHFMJ_2018_3_3_a5
E. A. Chirkova. Investigation of a 3D system of differential equations with non-isolated. Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 3, pp. 332-337. http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a5/

[1] Remizov A.O., “Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature”, Sbornik: Mathematics, 200:3 (2009), 385–403 | DOI | DOI | MR | Zbl

[2] Pavlova N.G., Remizov A.O., “Geodesics on hypersurfaces in Minkowski space: singularities of signature change”, Russian Mathematical Surveys, 66:6 (2011), 1201–1203 | DOI | DOI | MR | Zbl

[3] Pavlova N.G., Remizov A.O., “A complete classification of generic singularities of geodesic flows on 2-surfaces with pseudo-Riemannian metrics”, Russian Mathematical Surveys, 72:3 (2017), 577–579 | DOI | DOI | MR | Zbl

[4] Bruno A.D., Local method of nonlinear analysis for differential equations, Nauka Publ., Moscow, 1979, 25 pp. (In Russ.)

[5] Bruno A.D., Power geometry in algebraic and differential equations, Fizmathlit Publ., Moscow, 1998, 144 pp. (In Russ.) | MR

[6] Shilnikov L.P., Shilnikov A.L., Turaev D.V., Chua L., Methods of qualitative theory in nonlinear dynamics. Part 1., World Scientific Publ., Singapore, New Jersey, London, Hong Kong, 1998, 1113 pp. | MR