English

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}
}
R2 v1 2026-06-21T13:30:21.519Z