On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus

L. Asselle; G. Benedetti

doi:10.1007/s00209-016-1787-6

On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus

L. Asselle
, G. Benedetti

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

© 2016, Springer-Verlag Berlin Heidelberg.Let (T2, g) be a Riemannian two-torus and let σ be an oscillating 2-form on T2. We show that for almost every small positive number k the magnetic flow of the pair (g, σ) has infinitely many periodic orbits with energy k. This result complements the analogous statement for closed surfaces of genus at least 2 (Asselle and Benedetti in Calc Var Partial Differ Equ 54(2):1525–1545. doi:10.1007/s00526-015-0834-1, 2015) and at the same time extends the main theorem of Abbondandolo et al. (J Eur Math Soc, arXiv:1404.7641, to appear) to the non-exact oscillating case.

Original language	English
Pages (from-to)	843-859
Journal	Mathematische Zeitschrift
Volume	286
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-016-1787-6
Publication status	Published - 1 Aug 2017
Externally published	Yes

Funding

Luca Asselle is partially supported by the DFG Grant AB 360/2-1 “Periodic orbits of conservative systems below the Mañé critical energy value”. Gabriele Benedetti is partially supported by the DFG Grant SFB 878.

Funders	Funder number
Deutsche Forschungsgemeinschaft	SFB 878, AB 360/2-1

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AU - Asselle, L.

AU - Benedetti, G.

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N2 - © 2016, Springer-Verlag Berlin Heidelberg.Let (T2, g) be a Riemannian two-torus and let σ be an oscillating 2-form on T2. We show that for almost every small positive number k the magnetic flow of the pair (g, σ) has infinitely many periodic orbits with energy k. This result complements the analogous statement for closed surfaces of genus at least 2 (Asselle and Benedetti in Calc Var Partial Differ Equ 54(2):1525–1545. doi:10.1007/s00526-015-0834-1, 2015) and at the same time extends the main theorem of Abbondandolo et al. (J Eur Math Soc, arXiv:1404.7641, to appear) to the non-exact oscillating case.

AB - © 2016, Springer-Verlag Berlin Heidelberg.Let (T2, g) be a Riemannian two-torus and let σ be an oscillating 2-form on T2. We show that for almost every small positive number k the magnetic flow of the pair (g, σ) has infinitely many periodic orbits with energy k. This result complements the analogous statement for closed surfaces of genus at least 2 (Asselle and Benedetti in Calc Var Partial Differ Equ 54(2):1525–1545. doi:10.1007/s00526-015-0834-1, 2015) and at the same time extends the main theorem of Abbondandolo et al. (J Eur Math Soc, arXiv:1404.7641, to appear) to the non-exact oscillating case.

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On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus

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