Geodesic
Nonselfintersecting closed extremals of multivalued or not everywhere positive functionals
Izvestiya. Mathematics , Tome 38 (1992) no. 2, pp. 359-374.

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

A proof is given for the theorem of Novikov and the author on the existence of a closed nonselfintersecting extremal for a single-valued functional corresponding to the motion of a charged particle in a strong magnetic field on a Riemannian manifold homeomorphic to the 2-sphere, and an analogue in the case of multivalued functionals is also proved. 
@article{IM2_1992_38_2_a6,
     author = {I. A. Taimanov},
     title = {Nonselfintersecting closed extremals of multivalued or not everywhere positive functionals},
     journal = {Izvestiya. Mathematics },
     pages = {359--374},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_38_2_a6/}
}
TY  - JOUR
AU  - I. A. Taimanov
TI  - Nonselfintersecting closed extremals of multivalued or not everywhere positive functionals
JO  - Izvestiya. Mathematics 
PY  - 1992
SP  - 359
EP  - 374
VL  - 38
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1992_38_2_a6/
LA  - en
ID  - IM2_1992_38_2_a6
ER  - 
%0 Journal Article
%A I. A. Taimanov
%T Nonselfintersecting closed extremals of multivalued or not everywhere positive functionals
%J Izvestiya. Mathematics 
%D 1992
%P 359-374
%V 38
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1992_38_2_a6/
%G en
%F IM2_1992_38_2_a6
I. A. Taimanov. Nonselfintersecting closed extremals of multivalued or not everywhere positive functionals. Izvestiya. Mathematics , Tome 38 (1992) no. 2, pp. 359-374. http://geodesic.mathdoc.fr/item/IM2_1992_38_2_a6/

[1] Morse M., Calculus of variations in the large, Amer. Math. Soc. Colloq. Publ., 18, 1934 | MR | Zbl

[2] Lyusternik L. A., Shnirelman L. G., “Topologicheskie metody v variatsionnykh zadachakh i ikh prilozheniya k differentsialnoi geometrii poverkhnostei”, UMN, 2:1 (1947), 166–217 | MR

[3] Klingenberg V., Lektsii o zamknutykh geodezicheskikh, Mir, M., 1982 | MR | Zbl

[4] Lyusternik L. A., Fet A. I., “Variatsionnye zadachi na zamknutykh mnogoobraziyakh”, DAN SSSR, 81:1 (1951), 17–18 | MR | Zbl

[5] Serre J.-P., “Homologie singuliere des espaces fibres”, Ann. of Math., 54 (1951), 425–505 | DOI | MR | Zbl

[6] Novikov S. P., Shmeltser I., “Periodicheskie resheniya uravnenii Kirkhgofa dlya svobodnogo dvizheniya tvërdogo tela v zhidkosti i rasshirennaya teoriya Lyusternika–Shnirelmana–Morsa (LShM). I”, Funkts. analiz i ego prilozh., 15:3 (1981), 54–66 | MR

[7] Novikov S. P., “Variatsionnye metody i periodicheskie resheniya uravnenii tipa Kirkhgofa. II”, Funkts. analiz i ego prilozh., 15:4 (1981), 37–52 | MR

[8] Novikov S. P., “Mnogoznachnye funktsii i funktsionaly. Analog teorii Morsa”, DAN SSSR, 260:1 (1981), 31–34 | MR

[9] Novikov S. P., “Gamiltonov formalizm i mnogoznachnyi analog teorii Morsa”, UMN, 37:5 (1982), 3–49 | MR | Zbl

[10] Taimanov I. A., “Printsip perekidyvaniya tsiklov v teorii Morsa–Novikova”, DAN SSSR, 268:1 (1983), 46–50 | MR | Zbl

[11] Novikov S. P., Taimanov I. A., “Periodicheskie ekstremali mnogoznachnykh ili ne vsyudu polozhitelnykh funktsionalov”, DAN SSSR, 274:1 (1984), 26–28 | MR | Zbl

[12] Novikov S. P., “Algebraicheskaya topologiya v Matematicheskom institute im. V. A. Steklova AN SSSR”, Tr. MIAN, 169, 1985, 27–49 | Zbl

[13] Landau L. D., Lifshits E. M., Teoriya polya, Nauka, M., 1989

[14] Kozlov V. V., “Variatsionnoe ischislenie v tselom i klassicheskaya mekhanika”, UMN, 40:2 (1985), 33–60 | MR | Zbl

[15] Arnold V. I., “Pervye shagi simplekticheskoi topologii”, UMN, 41:6 (1986), 3–18 | MR

[16] Ginzburg V. L., “Novye obobscheniya geometricheskoi teoremy Puankare”, Funkts. analiz i ego prilozh., 21:2 (1987), 16–22 | MR | Zbl

[17] Grayson M. A., “Shortenning embedded curves”, Ann. of Math., 129 (1989), 71–111 | DOI | MR | Zbl

[18] Jost J., “A nonparametric proof of the theorem of Lusternik and Schnirelman”, Archiv der Mathematik, 53 (1989), 497–509 | DOI | MR | Zbl