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 Regul. Chaotic Dyn., 1997, Volume 2, Issue 1, Pages 3–12 (Mi rcd965)

Closed Orbits and Chaotic Dynamics of a Charged Particle in a Periodic Electromagnetic Field

V. V. Kozlov

119899, Russia, Moscow Vorobevy Gory, Moscow State University, Faculty of Mechanics and Mathematics, Department of Theoretical Mechanics

Abstract: We study motion of a charged particle on the two dimensional torus in a constant direction magnetic field. This analysis can be applied to the description of electron dynamics in metals, which admit a $2$-dimensional translation group (Bravais crystal lattice). We found the threshold magnetic value, starting from which there exist three closed Larmor orbits of a given energy. We demonstrate that if there are n lattice atoms in a primitive Bravais cell then there are $4+n$ different Larmor orbits in the nondegenerate case. If the magnetic field is absent the electron dynamics turns out to be chaotic, dynamical systems on the corresponding energy shells possess positive entropy in the case that the total energy is positive.

DOI: https://doi.org/10.1070/RD1997v002n01ABEH000021

Bibliographic databases:

Citation: V. V. Kozlov, “Closed Orbits and Chaotic Dynamics of a Charged Particle in a Periodic Electromagnetic Field”, Regul. Chaotic Dyn., 2:1 (1997), 3–12

Citation in format AMSBIB
\Bibitem{Koz97} \by V.~V.~Kozlov \paper Closed Orbits and Chaotic Dynamics of a Charged Particle in a Periodic Electromagnetic Field \jour Regul. Chaotic Dyn. \yr 1997 \vol 2 \issue 1 \pages 3--12 \mathnet{http://mi.mathnet.ru/rcd965} \crossref{https://doi.org/10.1070/RD1997v002n01ABEH000021} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1635176} \zmath{https://zbmath.org/?q=an:0937.37005} 

• http://mi.mathnet.ru/eng/rcd965
• http://mi.mathnet.ru/eng/rcd/v2/i1/p3

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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. Sergey P. Kuznetsov, “Hyperbolic Chaos in Self-oscillating Systems Based on Mechanical Triple Linkage: Testing Absence of Tangencies of Stable and Unstable Manifolds for Phase Trajectories”, Regul. Chaotic Dyn., 20:6 (2015), 649–666
2. S. P. Kuznetsov, “Giperbolicheskii khaos v avtokolebatelnykh sistemakh na osnove troinogo sharnirnogo mekhanizma: Proverka otsutstviya kasanii ustoichivykh i neustoichivykh mnogoobrazii fazovykh traektorii”, Nelineinaya dinam., 12:1 (2016), 121–143
3. Carles Simó, “Simple Flows on Tori with Uncommon Chaos”, Regul. Chaotic Dyn., 25:2 (2020), 199–214
4. S. P. Novikov, “Spinning tops and magnetic orbits”, Russian Math. Surveys, 75:6 (2020), 1133–1141