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

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...

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Vydané v:	Journal of mathematical analysis and applications Ročník 457; číslo 1; s. 568 - 584
Hlavní autori:	Cima, Anna, Gasull, Armengol, Mañosa, Víctor
Médium:	Journal Article Publikácia
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 01.01.2018
Predmet:	37 Dynamical systems and ergodic theory 37C Smooth dynamical systems: general theory 39 Difference and functional equations 39A Difference equations Bifurcació, Teoria de la Bifurcation Bifurcation theory Classificació AMS Cyclicity Difference equations Equacions diferencials i integrals Equacions en diferències Matemàtiques i estadística Non-hyperbolic fixed point Two periodic points Àrees temàtiques de la UPC Non-hyperbolic fixed point Bifurcation Cyclicity Two periodic points
ISSN:	0022-247X, 1096-0813
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Popis
Shrnutí:	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.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2017.08.029