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 Uspekhi Mat. Nauk, 1992, Volume 47, Issue 3(285), Pages 161–162 (Mi umn4521)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

Proof of S. P. Novikov's conjecture for the case of small perturbations of rational magnetic fields

I. A. Dynnikov

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English version:
Russian Mathematical Surveys, 1992, 47:3, 172–173

Bibliographic databases:

MSC: 57M10, 55Pxx, 57R40

Citation: I. A. Dynnikov, “Proof of S. P. Novikov's conjecture for the case of small perturbations of rational magnetic fields”, Uspekhi Mat. Nauk, 47:3(285) (1992), 161–162; Russian Math. Surveys, 47:3 (1992), 172–173

Citation in format AMSBIB
\Bibitem{Dyn92} \by I.~A.~Dynnikov \paper Proof of S.\,P.~Novikov's conjecture for the case of small perturbations of rational magnetic fields \jour Uspekhi Mat. Nauk \yr 1992 \vol 47 \issue 3(285) \pages 161--162 \mathnet{http://mi.mathnet.ru/umn4521} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1185309} \zmath{https://zbmath.org/?q=an:0778.58016} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992RuMaS..47..172D} \transl \jour Russian Math. Surveys \yr 1992 \vol 47 \issue 3 \pages 172--173 \crossref{https://doi.org/10.1070/RM1992v047n03ABEH000901} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992KU98000010} 

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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. I. A. Dynnikov, “S. P. Novikov's problem on the semiclassical motion of an electron”, Russian Math. Surveys, 48:2 (1993), 173–174
2. I. A. Dynnikov, “Proof of S. P. Novikov's conjecture on the semiclassical motion of an electron”, Math. Notes, 53:5 (1993), 495–501
3. S.P. Novikov, Andrei Ya. Mal'tsev, “Topological phenomena in normal metals”, Uspekhi Fizicheskikh Nauk, 168:3 (1998), 249
4. I. A. Dynnikov, “The geometry of stability regions in Novikov's problem on the semiclassical motion of an electron”, Russian Math. Surveys, 54:1 (1999), 21–59
5. Maltsev, AY, “Quasiperiodic functions and dynamical systems in quantum solid state physics”, Bulletin Brazilian Mathematical Society, 34:1 (2003), 171
6. Andrei Ya. Maltsev, “Quasiperiodic functions theory and the superlattice potentials for a two-dimensional electron gas”, J Math Phys (N Y ), 45:3 (2004), 1128
7. Maltsev, AY, “Dynamical systems, topology, and conductivity in normal metals”, Journal of Statistical Physics, 115:1–2 (2004), 31
8. I. A. Dynnikov, S. P. Novikov, “Topology of quasi-periodic functions on the plane”, Russian Math. Surveys, 60:1 (2005), 1–26
9. De Leo, R, “First-principles generation of stereographic maps for high-field magneto resistance in normal metals: An application to Au and Ag”, Physica B-Condensed Matter, 362:1–4 (2005), 62
10. De Leo, R, “Topology of plane sections of periodic polyhedra with an application to the truncated octahedron”, Experimental Mathematics, 15:1 (2006), 109
11. Maltsev A.Y., Novikov S.P., “Topology, quasiperiodic functions, and the transport phenomena”, Topology in Condensed Matter, Springer Series in Solid-State Sciences, 150, 2006, 31–59
12. Maltsev A.Ya., “Oscillation Phenomena and Experimental Determination of Exact Mathematical Stability Zones For Magneto-Conductivity in Metals Having Complicated Fermi Surfaces”, J. Exp. Theor. Phys., 125:5 (2017), 896–905
13. A. Ya. Maltsev, S. P. Novikov, “The theory of closed 1-forms, levels of quasiperiodic functions and transport phenomena in electron systems”, Proc. Steklov Inst. Math., 302 (2018), 279–297
14. Maltsev A.Ya., “The Second Boundaries of Stability Zones and the Angular Diagrams of Conductivity For Metals Having Complicated Fermi Surfaces”, J. Exp. Theor. Phys., 127:6 (2018), 1087–1111
15. A. Ya. Maltsev, S. P. Novikov, “Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter”, Russian Math. Surveys, 74:1 (2019), 141–173
16. Maltsev A.Ya., “the Complexity Classes of Angular Diagrams of the Metal Conductivity in Strong Magnetic Fields”, J. Exp. Theor. Phys., 129:1 (2019), 116–138
17. Novikov S.P. De Leo R. Dynnikov I.A. Maltsev A.Ya., “Theory of Dynamical Systems and Transport Phenomena in Normal Metals”, J. Exp. Theor. Phys., 129:4, SI (2019), 710–721
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