On first integrals of geodesic flows on a two-torus
Dynamical Systems
2017-12-19 v1 Differential Geometry
Abstract
The problem of the existence of an additional (independent on the energy) first integral, of a geodesic (or magnetic geodesic) flow, which is polynomial in momenta is studied. The relation of this problem to the existence of nontrivial solutions of stationary dispersionless limits of two-dimensional soliton equations is demonstrated. The nonexistence of an additional quadratic first integral is established for certain classes of magnetic geodesic flows.
Cite
@article{arxiv.1610.04822,
title = {On first integrals of geodesic flows on a two-torus},
author = {I. A. Taimanov},
journal= {arXiv preprint arXiv:1610.04822},
year = {2017}
}
Comments
28 pages