Integrable magnetic geodesic flows on 2-surfaces
Dynamical Systems
2023-03-29 v1 Analysis of PDEs
Differential Geometry
Symplectic Geometry
Abstract
We study the magnetic geodesic flows on 2-surfaces having an additional first integral which is independent of the Hamiltonian at a fixed energy level. The following two cases are considered: when there exists a quadratic in momenta integral, and also the case of a rational in momenta integral with a linear numerator and denominator. In both cases certain semi-Hamiltonian systems of PDEs appear. In this paper we construct exact solutions (generally speaking, local ones) to these systems: in the first case via the generalized hodograph method, in the second case via the Legendre transformation and the method of separation of variables.
Cite
@article{arxiv.2205.12499,
title = {Integrable magnetic geodesic flows on 2-surfaces},
author = {Sergei Agapov and Alexey Potashnikov and Vladislav Shubin},
journal= {arXiv preprint arXiv:2205.12499},
year = {2023}
}
Comments
22 pages