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arXiv · 0907.5088

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

Misha Bialy·Andrey E. Mironov
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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.

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Misha Bialy, Andrey E. Mironov. 2009-07-29. Rich quasi-linear system for integrable geodesic flows on 2-torus. https://arxiv.org/abs/0907.5088

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