On Local Description of Two-Dimensional Geodesic Flows with a Polynomial First Integral
Exactly Solvable and Integrable Systems
2016-04-20 v1 Mathematical Physics
Differential Geometry
Dynamical Systems
math.MP
Abstract
In this paper we construct multiparametric families of two dimensional metrics with polynomial first integral. Such integrable geodesic flows are described by solutions of some semi-Hamiltonian hydrodynamic type system. We find infinitely many conservation laws and commuting flows for this system. This procedure allows us to present infinitely many particular metrics by the generalized hodograph method.
Cite
@article{arxiv.1509.03084,
title = {On Local Description of Two-Dimensional Geodesic Flows with a Polynomial First Integral},
author = {Maxim V. Pavlov and Sergey P. Tsarev},
journal= {arXiv preprint arXiv:1509.03084},
year = {2016}
}
Comments
21 pages