Rich quasi-linear system for integrable geodesic flows on 2-torus

Details Rich quasi-linear system for integrable geodesic flows on 2-torus Rich quasi-linear system for integrable geodesic flows on 2-torus

2009-07-29

arxiv.org/abs/0907.5088v1

Mathematics

Differential Geometry

Scientific paper

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.

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