The quasiperiodic structure of level surfaces of a~Morse 1-form close to a~rational one~-- a~problem of S.\,P.~Novikov
Izvestiya. Mathematics , Tome 31 (1988) no. 3, pp. 635-655.

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

The topological structure is described of the level surfaces of a Morse 1-form which is close to a rational one on a closed oriented manifold. Applications are indicated to the investigation of the motion of an electron in a reciprocal lattice in a homogeneous magnetic field. Figures: 3. Bibliography: 11 titles.
@article{IM2_1988_31_3_a9,
     author = {A. V. Zorich},
     title = {The quasiperiodic structure of level surfaces of {a~Morse} 1-form close to a~rational one~-- a~problem of {S.\,P.~Novikov}},
     journal = {Izvestiya. Mathematics },
     pages = {635--655},
     publisher = {mathdoc},
     volume = {31},
     number = {3},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a9/}
}
TY  - JOUR
AU  - A. V. Zorich
TI  - The quasiperiodic structure of level surfaces of a~Morse 1-form close to a~rational one~-- a~problem of S.\,P.~Novikov
JO  - Izvestiya. Mathematics 
PY  - 1988
SP  - 635
EP  - 655
VL  - 31
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a9/
LA  - en
ID  - IM2_1988_31_3_a9
ER  - 
%0 Journal Article
%A A. V. Zorich
%T The quasiperiodic structure of level surfaces of a~Morse 1-form close to a~rational one~-- a~problem of S.\,P.~Novikov
%J Izvestiya. Mathematics 
%D 1988
%P 635-655
%V 31
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a9/
%G en
%F IM2_1988_31_3_a9
A. V. Zorich. The quasiperiodic structure of level surfaces of a~Morse 1-form close to a~rational one~-- a~problem of S.\,P.~Novikov. Izvestiya. Mathematics , Tome 31 (1988) no. 3, pp. 635-655. http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a9/

[1] Novikov S. P., “Mnogoznachnye funktsii i funktsionaly. Analog teorii Morsa”, Dokl. AN SSSR, 260:1 (1981), 31–35 | MR | Zbl

[2] Novikov S. P., “Gamiltonov formalizm i mnogoznachnyi analog teorii Morsa”, Uspekhi matem. nauk, 37:5(227) (1982), 3–49 | MR | Zbl

[3] Novikov S. P., “Kriticheskie tochki i poverkhnosti urovnya mnogoznachnykh funktsii”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 166, 1984, 201–209 | MR | Zbl

[4] Novikov S. P., Analog teorii Morsa dlya mnogoznachnykh funktsii. Nekotorye svoistva skobok Puassona; Б. А. Дубровин, С. П. Новиков, А. Т. Фоменко, Современная геометрия. Методы теории гомологии, Наука, М., 1984 | MR

[5] Milnor Dzh., Teorema ob $h$-kobordizme, Mir, M., 1969 | MR

[6] Milnor Dzh., Teoriya Morsa, Mir, M., 1965 | MR

[7] Fomenko A. T., Differentsialnaya geometriya i topologiya. Dopolnitelnye glavy, Mosk. un-t, M., 1983

[8] Pontryagin L. S., Nepreryvnye gruppy, Nauka, M., 1973 | MR | Zbl

[9] Tom Rene, Nekotorye svoistva “v tselom” differentsiruemykh mnogoobrazii. Rassloennye prostranstva i ikh prilozheniya, IL, M., 1958

[10] Farber M. Sh., “Tochnost neravenstv Novikova”, Funkts. analiz, 19:1 (1985), 49–60 | MR

[11] Zorich A. V., “Zadacha S. P. Novikova o poluklassicheskom dvizhenii elektrona v odnorodnom magnitnom pole, blizkom k ratsionalnomu”, Uspekhi matem. nauk, 39:5(239) (1984), 235–236 | MR | Zbl