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.
On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus / Asselle, L.; Benedetti, G.. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 286:3-4(2017), pp. 843-859. [10.1007/s00209-016-1787-6]
On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus
Asselle L.;Benedetti G.
2017-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
