Nonintegrabilty of a Halphen system

J. Llibre, C. Valls

Research output: Contribution to journalArticleResearchpeer-review


© 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)
Issue number2
Publication statusPublished - 1 Jan 2014


  • Halphen system
  • analytic first integral


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