Article Contents
Article Contents

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

• 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.
Mathematics Subject Classification: Primary: 37J35, 37K05, 37K10; Secondary: 35L67.

 Citation:

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