Nonintegrabilty of a Halphen system

J. Llibre, C. Valls

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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 languageEnglish
Pages (from-to)1383-1395
JournalTheoretical and Mathematical Physics(Russian Federation)
Volume181
Issue number2
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • analytic first integral
  • Halphen system

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    Llibre, J., & Valls, C. (2014). Nonintegrabilty of a Halphen system. Theoretical and Mathematical Physics(Russian Federation), 181(2), 1383-1395. https://doi.org/10.1007/s11232-014-0219-1