On polynomial integrability of the Euler equations on so(4)

Jaume Llibre; Jiang Yu; Xiang Zhang

doi:https://doi.org/10.1016/j.geomphys.2015.06.001

On polynomial integrability of the Euler equations on so(4)

Jaume Llibre, Jiang Yu, Xiang Zhang

Department of Mathematics

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

7 Citations (Scopus)

Abstract

© 2015 Elsevier B.V.. In this paper we prove that the Euler equations on the Lie algebra so(4) with a diagonal quadratic Hamiltonian either satisfy the Manakov condition, or have at most four functionally independent polynomial first integrals.

Original language	English
Pages (from-to)	36-41
Journal	Journal of Geometry and Physics
Volume	96
DOIs	https://doi.org/10.1016/j.geomphys.2015.06.001
Publication status	Published - 1 Oct 2015

Keywords

Analytic first integral
Euler equations
Kowalevsky exponent
Polynomial first integral
Quasi-homogeneous differential system

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https://doi.org/10.1016/j.geomphys.2015.06.001

https://ddd.uab.cat/record/145370

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title = "On polynomial integrability of the Euler equations on so(4)",

abstract = "{\textcopyright} 2015 Elsevier B.V.. In this paper we prove that the Euler equations on the Lie algebra so(4) with a diagonal quadratic Hamiltonian either satisfy the Manakov condition, or have at most four functionally independent polynomial first integrals.",

keywords = "Analytic first integral, Euler equations, Kowalevsky exponent, Polynomial first integral, Quasi-homogeneous differential system",

author = "Jaume Llibre and Jiang Yu and Xiang Zhang",

year = "2015",

month = oct,

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doi = "https://doi.org/10.1016/j.geomphys.2015.06.001",

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T1 - On polynomial integrability of the Euler equations on so(4)

AU - Llibre, Jaume

AU - Yu, Jiang

AU - Zhang, Xiang

PY - 2015/10/1

Y1 - 2015/10/1

N2 - © 2015 Elsevier B.V.. In this paper we prove that the Euler equations on the Lie algebra so(4) with a diagonal quadratic Hamiltonian either satisfy the Manakov condition, or have at most four functionally independent polynomial first integrals.

AB - © 2015 Elsevier B.V.. In this paper we prove that the Euler equations on the Lie algebra so(4) with a diagonal quadratic Hamiltonian either satisfy the Manakov condition, or have at most four functionally independent polynomial first integrals.

KW - Analytic first integral

KW - Euler equations

KW - Kowalevsky exponent

KW - Polynomial first integral

KW - Quasi-homogeneous differential system

U2 - https://doi.org/10.1016/j.geomphys.2015.06.001

DO - https://doi.org/10.1016/j.geomphys.2015.06.001

M3 - Article

SN - 0393-0440

VL - 96

SP - 36

EP - 41

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -

On polynomial integrability of the Euler equations on so(4)

Abstract

Keywords

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