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

Misha Bialy; Andrey E. Mironov

doi:10.3934/dcds.2011.29.81

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

Misha Bialy, Andrey E. Mironov

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

Consider a Riemannian metric on two-torus. We prove that the question of existence of polynomial first integrals leads naturally to a remark- able 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.

Original language	English
Pages (from-to)	81-90
Number of pages	10
Journal	Discrete and Continuous Dynamical Systems
Volume	29
Issue number	1
DOIs	https://doi.org/10.3934/dcds.2011.29.81
State	Published - 1 Jan 2011

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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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 remark- able 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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AB - Consider a Riemannian metric on two-torus. We prove that the question of existence of polynomial first integrals leads naturally to a remark- able 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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JO - Discrete and Continuous Dynamical Systems

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

Abstract

All Science Journal Classification (ASJC) codes

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