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Uspekhi Mat. Nauk, 1999, Volume 54, Issue 1(325), Pages 21–60 (Mi umn116)  

This article is cited in 28 scientific papers (total in 28 papers)

The geometry of stability regions in Novikov's problem on the semiclassical motion of an electron

I. A. Dynnikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

DOI: https://doi.org/10.4213/rm116

Full text: PDF file (1232 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1999, 54:1, 21–59

Bibliographic databases:

UDC: 517.98
MSC: Primary 57R70; Secondary 58E05, 57R30, 81Q20, 81V10, 78A35
Received: 15.01.1999

Citation: I. A. Dynnikov, “The geometry of stability regions in Novikov's problem on the semiclassical motion of an electron”, Uspekhi Mat. Nauk, 54:1(325) (1999), 21–60; Russian Math. Surveys, 54:1 (1999), 21–59

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. P. Novikov, “Levels of quasiperiodic functions on a plane, and Hamiltonian systems”, Russian Math. Surveys, 54:5 (1999), 1031–1032  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. R. De Leo, “The existence and measure of ergodic foliations in Novikov's problem of the semiclassical motion of an electron”, Russian Math. Surveys, 55:1 (2000), 166–168  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Novikov S.P., “1. Classical and modern topology 2. Topological phenomena in real world physics”, GAFA 2000 (Tel Aviv, 1999), Geom. Funct. Anal., 2000, 406–424  mathscinet  zmath  isi
    4. R. De Leo, “Characterization of the set of “ergodic directions” in Novikov's problem of quasi-electron orbits in normal metals”, Russian Math. Surveys, 58:5 (2003), 1042–1043  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. De Leo R., “Numerical analysis of the Novikov problem of a normal metal in a strong magnetic field”, SIAM J. Appl. Dyn. Syst., 2:4 (2003), 517–545  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    6. Maltsev A.Yu., Novikov S.P., “Quasiperiodic functions and dynamical systems in quantum solid state physics”, Bull. Braz. Math. Soc. (N.S.), 34:1 (2003), 171–210  crossref  mathscinet  zmath  isi  elib
    7. Maltsev A.Ya., “Quasiperiodic functions theory and the superlattice potentials for a two-dimensional electron gas”, J. Math. Phys., 45:3 (2004), 1128–1149  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    8. De Leo R., “Topological effects in the magnetoresi stance of Au and Ag”, Phys. Lett. A, 332:5-6 (2004), 469–474  crossref  zmath  adsnasa  isi  scopus  scopus
    9. Maltsev A.Yu., Novikov S.P., “Dynamical systems, topology, and conductivity in normal metals”, J. Statist. Phys., 115:1-2 (2004), 31–46  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. I. A. Dynnikov, S. P. Novikov, “Topology of quasi-periodic functions on the plane”, Russian Math. Surveys, 60:1 (2005), 1–26  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. R. De Leo, “Proof of Dynnikov's conjecture on the location of stability zones in the Novikov problem on planar sections of periodic surfaces”, Russian Math. Surveys, 60:3 (2005), 566–567  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    12. 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: Physics of Condensed Matter, 362:1-4 (2005), 62–75  crossref  adsnasa  isi  scopus  scopus
    13. Gelbukh I., “Presence of minimal components in a Morse form foliation”, Differential Geom. Appl., 22:2 (2005), 189–198  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    14. De Leo R., “Topology of plane sections of periodic polyhedra with an application to the truncated octahedron”, Experiment. Math., 15:1 (2006), 109–124  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    15. 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  crossref  mathscinet  zmath  adsnasa  isi
    16. Zorich A., “Flat surfaces”, Frontiers in Number Theory, Physics and Geometry I - ON RANDOM MATRICES, ZETA FUNCTIONS, AND DYNAMICAL SYSTEMS, 2006, 439–585  crossref  mathscinet  isi
    17. R. De Leo, I. A. Dynnikov, “An example of a fractal set of plane directions having chaotic intersections with a fixed 3-periodic surface”, Russian Math. Surveys, 62:5 (2007), 990–992  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. Millionschikov D.V., “Multi-valued functionals, one-forms and deformed de Rham complex”, Topology in Molecular Biology, Biological and Medical Physics, Biomedical Engineering, 2007, 189–208  crossref  adsnasa  isi
    19. I. A. Dynnikov, “Interval Identification Systems and Plane Sections of 3-Periodic Surfaces”, Proc. Steklov Inst. Math., 263 (2008), 65–77  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    20. DeLeo R., Dynnikov I.A., “Geometry of plane sections of the infinite regular skew polyhedron ${4,6\mid 4}$”, Geom. Dedicata, 138:1 (2009), 51–67  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    21. 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  crossref  isi  scopus  scopus
    22. Maltsev A.Ya., “On the Analytical Properties of the Magneto-Conductivity in the Case of Presence of Stable Open Electron Trajectories on a Complex Fermi Surface”, J. Exp. Theor. Phys., 124:5 (2017), 805–831  crossref  isi  scopus  scopus
    23. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    24. 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  crossref  isi  scopus
    25. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    26. De Leo R. Maltsev A.Y., “Quasiperiodic Dynamics and Magnetoresistance in Normal Metals”, Acta Appl. Math., 162:1 (2019), 47–61  crossref  isi
    27. 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  crossref  isi
    28. 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  crossref  isi
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