Center-focus and isochronous center problems for discontinuous differential equations

B. Coll, A. Gasull, R. Prohens

Research output: Contribution to journalArticleResearchpeer-review

12 Citations (Scopus)

Abstract

The study of the center focus problem and the isochronicity problem for differential equations with a line of discontinuities is usually done by computing the whole return map as the composition of the two maps associated to the two smooth differential equations. This leads to large formulas which usually are treated with algebraic manipulators. In this paper we approach to this problem from a more theoretical point of view. The results that we obtain relate the order of degeneracy of the critical point of the discontinuous differential equations with the order of degeneracy of the two smooth component differential equations. Finally we apply them to some families of examples.
Original languageEnglish
Pages (from-to)609-624
JournalDiscrete and Continuous Dynamical Systems
Volume6
Issue number3
Publication statusPublished - 1 Jul 2000

Keywords

  • Center point
  • Discontinuous differential equation
  • Isochronicity

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