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

Anna Cima; Armengol Gasull; Víctor Mañosa

doi:https://doi.org/10.1016/j.jmaa.2017.08.029

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

Anna Cima, Armengol Gasull, Víctor Mañosa

Research output: Contribution to journal › Article › Research › peer-review

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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 language	English
Pages (from-to)	568-584
Journal	Journal of Mathematical Analysis and Applications
Volume	457
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2017.08.029
Publication status	Published - 1 Jan 2018

Keywords

Bifurcation
Cyclicity
Non-hyperbolic fixed point
Two periodic points

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Cite this

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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.",

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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

U2 - https://doi.org/10.1016/j.jmaa.2017.08.029

DO - https://doi.org/10.1016/j.jmaa.2017.08.029

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EP - 584

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

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ER -

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

Abstract

Keywords

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