DCDS
Rich quasi-linear system for integrable geodesic flows on 2-torus
Misha Bialy Andrey E. Mironov
Discrete & Continuous Dynamical Systems - A 2011, 29(1): 81-90 doi: 10.3934/dcds.2011.29.81
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: Polynomial integrals Riemann invariants Geodesic flows Rich systems. genuine nonlinearity

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