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

Anna Cima; Armengol Gasull; Víctor Mañosa

doi:10.1016/j.jmaa.2017.08.029

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

Anna Cima, Armengol Gasull, Víctor Mañosa

Departament de Matemàtiques

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Resum

© 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.

Idioma original	Anglès
Pàgines (de-a)	568-584
Revista	Journal of Mathematical Analysis and Applications
Volum	457
Número	1
DOIs	https://doi.org/10.1016/j.jmaa.2017.08.029
Estat de la publicació	Publicada - 1 de gen. 2018

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10.1016/j.jmaa.2017.08.029

https://ddd.uab.cat/record/182539

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https://www.scopus.com/pages/publications/85028465344

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title = "Bifurcation of 2-periodic orbits from non-hyperbolic fixed points",

abstract = "{\textcopyright} 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.",

keywords = "Bifurcation, Cyclicity, Non-hyperbolic fixed point, Two periodic points",

author = "Anna Cima and Armengol Gasull and V{\'i}ctor Ma{\~n}osa",

year = "2018",

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AU - Cima, Anna

AU - Gasull, Armengol

AU - Mañosa, Víctor

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Y1 - 2018/1/1

N2 - © 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.

AB - © 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.

KW - Bifurcation

KW - Cyclicity

KW - Non-hyperbolic fixed point

KW - Two periodic points

UR - https://www.scopus.com/pages/publications/85028465344

U2 - 10.1016/j.jmaa.2017.08.029

DO - 10.1016/j.jmaa.2017.08.029

M3 - Article

SN - 0022-247X

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SP - 568

EP - 584

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

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

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