The criticality of centers of potential systems at the outer boundary

F. Mañosas, D. Rojas, J. Villadelprat

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Abstract

© 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
Volume260
Issue number6
DOIs
Publication statusPublished - 15 Mar 2016

Keywords

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

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    Mañosas, F., Rojas, D., & Villadelprat, J. (2016). The criticality of centers of potential systems at the outer boundary. Journal of Differential Equations, 260(6), 4918-4972. https://doi.org/10.1016/j.jde.2015.11.040