The criticality of centers of potential systems at the outer boundary

F. Mañosas, D. Rojas, J. Villadelprat

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10 Citations (Scopus)


© 2015 Elsevier Inc. The number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied. We call this number the criticality at the outer boundary. Our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1. We apply them to study the bifurcation diagram of the period function of X=-y∂x+((x+1)p-(x+1)q)∂y with q<p. This family was previously studied for q=1 by Y. Miyamoto and K. Yagasaki.
Original languageEnglish
Pages (from-to)4918-4972
JournalJournal of Differential Equations
Issue number6
Publication statusPublished - 15 Mar 2016


  • Bifurcation
  • Center
  • Critical periodic orbit
  • Criticality
  • Period function


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