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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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 457; no. 1; pp. 568 - 584
Main Authors: Cima, Anna, Gasull, Armengol, Mañosa, Víctor
Format: Journal Article Publication
Language:English
Published: Elsevier Inc 01.01.2018
Subjects:
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
Online Access:Get full text
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Summary: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