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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 6, Pages 1322–1344 (Mi izv1343)  

This article is cited in 4 scientific papers (total in 4 papers)

The quasiperiodic structure of level surfaces of a Morse 1-form close to a rational one – a problem of S. P. Novikov

A. V. Zorich


Abstract: 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.

Full text: PDF file (3468 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1988, 31:3, 635–655

Bibliographic databases:

UDC: 514.76+515.16
MSC: Primary 58E05; Secondary 58F05
Received: 18.06.1985

Citation: 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”, Izv. Akad. Nauk SSSR Ser. Mat., 51:6 (1987), 1322–1344; Math. USSR-Izv., 31:3 (1988), 635–655

Citation in format AMSBIB
\Bibitem{Zor87}
\by A.~V.~Zorich
\paper The quasiperiodic structure of level surfaces of a~Morse 1-form close to a~rational one~-- a~problem of S.\,P.~Novikov
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 6
\pages 1322--1344
\mathnet{http://mi.mathnet.ru/izv1343}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=933967}
\zmath{https://zbmath.org/?q=an:0694.58002|0668.58004}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 31
\issue 3
\pages 635--655
\crossref{https://doi.org/10.1070/IM1988v031n03ABEH001094}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. A. Alaniya, “The topological structure of level surfaces of Morse 1-forms”, Russian Math. Surveys, 46:3 (1991), 211–212  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. A. Dynnikov, “Proof of S. P. Novikov's conjecture for the case of small perturbations of rational magnetic fields”, Russian Math. Surveys, 47:3 (1992), 172–173  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. I. A. Melnikova, “A test for compactness of a foliation”, Math. Notes, 58:6 (1995), 1302–1305  mathnet  crossref  mathscinet  zmath  isi
    4. I. A. Melnikova, “A test for non-compactness of the foliation of a Morse form”, Russian Math. Surveys, 50:2 (1995), 444–445  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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