Yuri A. Kordyukov, Iskander A. Taimanov, “Trace Formula for the Magnetic Laplacian on a Compact Hyperbolic Surface”, Regul. Chaotic Dyn., 2022, Volume 27, Issue 4,Pages <nobr>460

This article is cited in 3 papers

Alexey Borisov Memorial Volume

Trace Formula for the Magnetic Laplacian on a Compact Hyperbolic Surface

Yuri A. Kordyukov^a, Iskander A. Taimanov^bc

^a Institute of Mathematics, Ufa Federal Research Centre, Russian Academy of Sciences, ul. Chernyshevskogo 112, 450008 Ufa, Russia
^b Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, 630090 Novosibirsk, Russia
^c Novosibirsk State University, ul. Pirogova 1, 630090 Novosibirsk, Russia

Abstract: We compute the trace formula for the magnetic Laplacian on a compact hyperbolic surface of constant curvature with a constant magnetic field for energies above the Mane critical level of the corresponding magnetic geodesic flow. We discuss the asymptotic behavior of the coefficients of the trace formula when the energy approaches the Mane critical level.

Keywords: trace formula, magnetic Laplacian, magnetic geodesic flow.

MSC: 58J50, 37J35, 58J37, 81Q20

Received: 14.02.2022
Accepted: 18.04.2022

Language: English

DOI: 10.1134/S1560354722040050