The Michelson system is neither global analytic, nor Darboux integrable

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

We consider the differential system over(x, ̇) = y, over(y, ̇) = z, over(z, ̇) = c2 - y - x2 / 2 in R3, where c is a real parameter. This differential system is known as the Michelson system and its dynamics has been studied during these last twenty five years but nothing was known up to now on its integrability. We show that for any value of c the Michelson system is neither global analytic, nor Darboux integrable. © 2010 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)414-419
JournalPhysica D: Nonlinear Phenomena
Volume239
DOIs
Publication statusPublished - 15 Apr 2010

Keywords

  • Analytic integrability
  • Darboux integrability
  • Darboux polynomials
  • Exponential factors
  • Michelson system
  • Polynomial integrability
  • Rational integrability

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