Basin of attraction of triangular maps with applications

Anna Cima; Armengol Gasull; Víctor Mañosa

doi:10.1080/10236198.2013.852187

Basin of attraction of triangular maps with applications

Anna Cima, Armengol Gasull, Víctor Mañosa

Department of Mathematics

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

3 Citations (Scopus)

Abstract

We consider planar triangular maps. These maps preserve the fibration of the plane given by. We assume that there exists an invariant attracting fibre for the dynamical system generated by φ, and we study the limit dynamics of those points in the basin of attraction of this invariant fibre, assuming that either it contains a global attractor or it is filled by fixed or two-periodic points. We apply our results to several examples. © 2014 © 2014 Taylor & Francis.

Original language	English
Pages (from-to)	423-437
Journal	Journal of Difference Equations and Applications
Volume	20
Issue number	3
DOIs	https://doi.org/10.1080/10236198.2013.852187
Publication status	Published - 1 Mar 2014

Keywords

attractors
difference equations
discrete dynamical systems
periodic solutions
quasi-homogeneous maps
triangular maps

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N2 - We consider planar triangular maps. These maps preserve the fibration of the plane given by. We assume that there exists an invariant attracting fibre for the dynamical system generated by φ, and we study the limit dynamics of those points in the basin of attraction of this invariant fibre, assuming that either it contains a global attractor or it is filled by fixed or two-periodic points. We apply our results to several examples. © 2014 © 2014 Taylor & Francis.

AB - We consider planar triangular maps. These maps preserve the fibration of the plane given by. We assume that there exists an invariant attracting fibre for the dynamical system generated by φ, and we study the limit dynamics of those points in the basin of attraction of this invariant fibre, assuming that either it contains a global attractor or it is filled by fixed or two-periodic points. We apply our results to several examples. © 2014 © 2014 Taylor & Francis.

KW - attractors

KW - difference equations

KW - discrete dynamical systems

KW - periodic solutions

KW - quasi-homogeneous maps

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