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...

Descripción completa

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
_version_ 1782439222444032000
author Deng, Xiaocheng
Meng, Fanning
Lin, Jianming
Yuan, Wenjun
author_facet Deng, Xiaocheng
Meng, Fanning
Lin, Jianming
Yuan, Wenjun
author_sort Deng, Xiaocheng
collection PubMed
description 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.
format Online
Article
Text
id pubmed-4919272
institution National Center for Biotechnology Information
language English
publishDate 2016
publisher Springer International Publishing
record_format MEDLINE/PubMed
spelling pubmed-49192722016-07-06 Dynamics of the functions [Formula: see text] with the real parameter Deng, Xiaocheng Meng, Fanning Lin, Jianming Yuan, Wenjun Springerplus Research 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. Springer International Publishing 2016-06-23 /pmc/articles/PMC4919272/ /pubmed/27386299 http://dx.doi.org/10.1186/s40064-016-2411-2 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Deng, Xiaocheng
Meng, Fanning
Lin, Jianming
Yuan, Wenjun
Dynamics of the functions [Formula: see text] with the real parameter
title Dynamics of the functions [Formula: see text] with the real parameter
title_full Dynamics of the functions [Formula: see text] with the real parameter
title_fullStr Dynamics of the functions [Formula: see text] with the real parameter
title_full_unstemmed Dynamics of the functions [Formula: see text] with the real parameter
title_short Dynamics of the functions [Formula: see text] with the real parameter
title_sort dynamics of the functions [formula: see text] with the real parameter
topic Research
url 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
work_keys_str_mv AT dengxiaocheng dynamicsofthefunctionsformulaseetextwiththerealparameter
AT mengfanning dynamicsofthefunctionsformulaseetextwiththerealparameter
AT linjianming dynamicsofthefunctionsformulaseetextwiththerealparameter
AT yuanwenjun dynamicsofthefunctionsformulaseetextwiththerealparameter

Ejemplares similares