First derivative of the period function with applications

Armengol Gasull, Emilio Freire, Antoni Guillamon

Research output: Contribution to journalArticleResearchpeer-review

37 Citations (Scopus)


Given a centre of a planar differential system, we extend the use of the Lie bracket to the determination of the monotonicity character of the period function. As far as we know, there are no general methods to study this function, and the use of commutators and Lie bracket was restricted to prove isochronicity. We give several examples and a special method which simplifies the computations when a first integral is known. © 2004 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)139-162
JournalJournal of Differential Equations
Publication statusPublished - 10 Sep 2004


  • Center
  • Lie symmetries
  • Period function
  • Planar system


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