Rich quasi-linear system for integrable geodesic flows on 2-torus
Differential Geometry
2009-07-30 v1 Analysis of PDEs
Abstract
Consider a Riemannian metric on two-torus. We prove that the question of existence of polynomial first integrals leads naturally to a remarkable system of quasi-linear equations which turns out to be a Rich system of conservation laws. This reduces the question of integrability to the question of existence of smooth (quasi-) periodic solutions for this Rich quasi-linear system.
Keywords
Cite
@article{arxiv.0907.5088,
title = {Rich quasi-linear system for integrable geodesic flows on 2-torus},
author = {Misha Bialy and Andrey E. Mironov},
journal= {arXiv preprint arXiv:0907.5088},
year = {2009}
}