Nonintegrabilty of a Halphen system

J. Llibre; C. Valls

doi:https://doi.org/10.1007/s11232-014-0219-1

Nonintegrabilty of a Halphen system

J. Llibre, C. Valls

Department of Mathematics

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

Abstract

© 2014, Pleiades Publishing, Ltd. We study the Halphen system with real variables and real constants. We show that in the case where at least one constant is nonzero, this system does not admit any first integral that can be described by formal power series. It hence follows that analytic first integrals do not exist. Furthermore, we prove that first integrals of the Darboux type also do not exist.

Original language	English
Pages (from-to)	1383-1395
Journal	Theoretical and Mathematical Physics(Russian Federation)
Volume	181
Issue number	2
DOIs	https://doi.org/10.1007/s11232-014-0219-1
Publication status	Published - 1 Jan 2014

Keywords

Halphen system
analytic first integral

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https://ddd.uab.cat/record/150694

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title = "Nonintegrabilty of a Halphen system",

abstract = "{\textcopyright} 2014, Pleiades Publishing, Ltd. We study the Halphen system with real variables and real constants. We show that in the case where at least one constant is nonzero, this system does not admit any first integral that can be described by formal power series. It hence follows that analytic first integrals do not exist. Furthermore, we prove that first integrals of the Darboux type also do not exist.",

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AU - Valls, C.

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N2 - © 2014, Pleiades Publishing, Ltd. We study the Halphen system with real variables and real constants. We show that in the case where at least one constant is nonzero, this system does not admit any first integral that can be described by formal power series. It hence follows that analytic first integrals do not exist. Furthermore, we prove that first integrals of the Darboux type also do not exist.

AB - © 2014, Pleiades Publishing, Ltd. We study the Halphen system with real variables and real constants. We show that in the case where at least one constant is nonzero, this system does not admit any first integral that can be described by formal power series. It hence follows that analytic first integrals do not exist. Furthermore, we prove that first integrals of the Darboux type also do not exist.

KW - Halphen system

KW - analytic first integral

U2 - https://doi.org/10.1007/s11232-014-0219-1

DO - https://doi.org/10.1007/s11232-014-0219-1

M3 - Article

VL - 181

SP - 1383

EP - 1395

IS - 2

ER -

Nonintegrabilty of a Halphen system

Abstract

Keywords

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