Bifurcation of 2-periodic orbits from non-hyperbolic fixed points

Anna Cima, Armengol Gasull, Víctor Mañosa

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1 Citation (Scopus)

Abstract

© 2017 Elsevier Inc. We introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful in order to study the number of 2-periodic orbits that can bifurcate from the fixed point. As an application we study the 2-cyclicity of some natural families of polynomial maps.
Original languageEnglish
Pages (from-to)568-584
JournalJournal of Mathematical Analysis and Applications
Volume457
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • Bifurcation
  • Cyclicity
  • Non-hyperbolic fixed point
  • Two periodic points

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