Legendre Singularities in Systems of Implicit ODEs and Slow–Fast Dynamical Systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 261 (2008), pp. 140-153 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Generic properties of regular first integrals of systems of implicit differential equations are considered. In particular, for systems of two equations with two phase variables, a classification of generic bifurcations of integral level surfaces is described.
@article{TM_2008_261_a10,
     author = {V. M. Zakalyukin and A. O. Remizov},
     title = {Legendre {Singularities} in {Systems} of {Implicit} {ODEs} and {Slow{\textendash}Fast} {Dynamical} {Systems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {140--153},
     year = {2008},
     volume = {261},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_261_a10/}
}
TY  - JOUR
AU  - V. M. Zakalyukin
AU  - A. O. Remizov
TI  - Legendre Singularities in Systems of Implicit ODEs and Slow–Fast Dynamical Systems
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2008
SP  - 140
EP  - 153
VL  - 261
UR  - http://geodesic.mathdoc.fr/item/TM_2008_261_a10/
LA  - ru
ID  - TM_2008_261_a10
ER  - 
%0 Journal Article
%A V. M. Zakalyukin
%A A. O. Remizov
%T Legendre Singularities in Systems of Implicit ODEs and Slow–Fast Dynamical Systems
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2008
%P 140-153
%V 261
%U http://geodesic.mathdoc.fr/item/TM_2008_261_a10/
%G ru
%F TM_2008_261_a10
V. M. Zakalyukin; A. O. Remizov. Legendre Singularities in Systems of Implicit ODEs and Slow–Fast Dynamical Systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 261 (2008), pp. 140-153. http://geodesic.mathdoc.fr/item/TM_2008_261_a10/

[1] Arnold V. I., Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1978 | MR

[2] Arnold V. I., Geometricheskie metody v teorii obyknovennykh differentsialnykh uravnenii, Izd-vo Udmurt. gos. un-ta, Izhevsk, 2000

[3] Arnold V. I., “Kontaktnaya struktura, relaksatsionnye kolebaniya i osobye tochki neyavnykh differentsialnykh uravnenii”, Izbrannoe – 60, Fazis, M., 1997, 391–396 | MR

[4] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii. Klassifikatsiya kriticheskikh tochek, kaustik i volnovykh frontov, Nauka, M., 1982 | MR

[5] Arnold V. I., Afraimovich V. S., Ilyashenko Yu. S., Shilnikov L. P., “Teoriya bifurkatsii”, Dinamicheskie sistemy – 5, Itogi nauki i tekhniki. Sovr. probl. matematiki. Fund. napr., 5, VINITI, M., 1986, 5–218 | MR

[6] Davydov A. A., “Normalnaya forma medlennykh dvizhenii uravneniya relaksatsionnogo tipa i rassloeniya binomialnykh poverkhnostei”, Mat. sb., 132:1 (1987), 131–139 | MR | Zbl

[7] Givental A. B., “Osobye lagranzhevy mnogoobraziya i ikh lagranzhevy otobrazheniya”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Noveishie dostizheniya, 33, VINITI, M., 1988, 55–112 | MR

[8] Ishikawa G., “Symplectic and Lagrange stabilities of open Whitney umbrellas”, Invent. math., 126:2 (1996), 215–234 | DOI | MR | Zbl

[9] Lemasurier M., “Singularities of second-order implicit differential equations: a geometrical approach”, J. Dyn. and Control Syst., 7:2 (2001), 277–298 | DOI | MR | Zbl

[10] Piliya A. D., Fedorov V. I., “Osobennosti polya elektromagnitnoi volny v kholodnoi anizotropnoi plazme s dvumernoi neodnorodnostyu”, ZhETF, 60:1 (1971), 389–399

[11] Puankare A., O krivykh, opredelyaemykh differentsialnymi uravneniyami, Gostekhizdat, M., L., 1947

[12] Puankare A., Izbrannye trudy, T. 3, Nauka, M., 1974

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

[14] Remizov A. O., “O tipichnykh osobykh tochkakh neyavnykh differentsialnykh uravnenii”, Vestn. Mosk. un-ta. Matematika. Mekhanika, 2002, no. 5, 10–16 | MR | Zbl

[15] Remizov A. O., “Neyavnye differentsialnye uravneniya i vektornye polya s neizolirovannymi osobymi tochkami”, Mat. sb., 193:11 (2002), 105–124 | MR | Zbl

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

[17] Takens F., “Constrained equations; a study of implicit differential equations and their discontinuous solutions”, Structural stability, the theory of catastrophes, and applications in the sciences, Lect. Notes Math., 525, Springer, Berlin, 1976, 143–234 | MR

[18] Zakalyukin V. M., “Odno obobschenie lagranzhevykh triad”, UMN, 41:4 (1986), 180

[19] Zakalyukin V. M., “Perestroiki frontov, kaustik, zavisyaschikh ot parametra, versalnost otobrazhenii”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Noveishie dostizheniya, 22, VINITI, M., 1983, 56–93 | MR