Dynamics of the functions [Formula: see text] with the real parameter

In this paper, the dynamics of the functions [Formula: see text] with the real parameter is studied. We say that a real parameter [Formula: see text] belongs to the set [Formula: see text] for a positive integer n if [Formula: see text] has an attracting cycle of n-order. We prove that the Fatou set...

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Detalles Bibliográficos
Autores principales: Deng, Xiaocheng, Meng, Fanning, Lin, Jianming, Yuan, Wenjun
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4919272/
https://www.ncbi.nlm.nih.gov/pubmed/27386299
http://dx.doi.org/10.1186/s40064-016-2411-2
Descripción
Sumario:In this paper, the dynamics of the functions [Formula: see text] with the real parameter is studied. We say that a real parameter [Formula: see text] belongs to the set [Formula: see text] for a positive integer n if [Formula: see text] has an attracting cycle of n-order. We prove that the Fatou set [Formula: see text] is a completely invariant attracting basin for every parameter [Formula: see text] . Further, regarding the set [Formula: see text] for [Formula: see text] , we prove the following results: (1) There exists [Formula: see text] such that [Formula: see text] . (2) For every positive integer [Formula: see text] , the set [Formula: see text] is non-empty. (3) For every prime number [Formula: see text] , the set [Formula: see text] has at least two components.

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