On the polynomial integrability of a system motivated by the Riemann ellipsoid problem

Jaume Llibre; Clàudia Valls

doi:10.1051/cocv/2015035

On the polynomial integrability of a system motivated by the Riemann ellipsoid problem

Jaume Llibre, Clàudia Valls

Department of Mathematics

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

Abstract

© EDP Sciences, SMAI 2016. We consider differential systems obtained by coupling two Euler-Poinsot systems. The motivation to consider such systems can be traced back to the Riemann ellipsoid problem. We provide new cases for which these systems are completely integrable. We also prove that these systems either are completely integrable or have at most four functionally independent analytic first integrals.

Original language	English
Pages (from-to)	872-882
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	22
Issue number	3
DOIs	https://doi.org/10.1051/cocv/2015035
Publication status	Published - 1 Jul 2016

Keywords

Complete integrability
Euler-Poinsot systems
Homogeneous differential systems
Polynomial first integrals
Riemann ellipsoid problem

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abstract = "{\textcopyright} EDP Sciences, SMAI 2016. We consider differential systems obtained by coupling two Euler-Poinsot systems. The motivation to consider such systems can be traced back to the Riemann ellipsoid problem. We provide new cases for which these systems are completely integrable. We also prove that these systems either are completely integrable or have at most four functionally independent analytic first integrals.",

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AU - Valls, Clàudia

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N2 - © EDP Sciences, SMAI 2016. We consider differential systems obtained by coupling two Euler-Poinsot systems. The motivation to consider such systems can be traced back to the Riemann ellipsoid problem. We provide new cases for which these systems are completely integrable. We also prove that these systems either are completely integrable or have at most four functionally independent analytic first integrals.

AB - © EDP Sciences, SMAI 2016. We consider differential systems obtained by coupling two Euler-Poinsot systems. The motivation to consider such systems can be traced back to the Riemann ellipsoid problem. We provide new cases for which these systems are completely integrable. We also prove that these systems either are completely integrable or have at most four functionally independent analytic first integrals.

KW - Complete integrability

KW - Euler-Poinsot systems

KW - Homogeneous differential systems

KW - Polynomial first integrals

KW - Riemann ellipsoid problem

U2 - 10.1051/cocv/2015035

DO - 10.1051/cocv/2015035

M3 - Article

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EP - 882

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

SN - 1292-8119

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