On the Dynamics of Entire Maps with Symmetry
Cao, Chun-Lei1; Wang, Yue-Fei2,3
AbstractThis paper presents a detailed study of the dynamics of transcendental entire maps which are symmetric with respect to rays of the form Lambda(a, theta) = {te(i theta) + a vertical bar t >= 0}, with a epsilon C and theta epsilon [0, 2 pi). The symmetric families considered in the paper contain many well-known entire maps. Let f be such a symmetric entire map. Then (i) there exists a point z(0) = t(0e)(i theta) + a, (t(0) >= 0), such that for every point z on the ray Lambda(0)(a, theta) = {te(i theta) + a vertical bar t >= t(0)}, and any point zn in its forward orbit, any connected compact set containing z and zn must intersect the Julia set of f; (ii) The map f either has a multiply-connected wandering domain, or its Julia set contains the ray Lambda(0)(a, theta); (iii) If t(0) > 0, then the Fatou set of f has an invariant immediate attractive basin, or an invariant Leau domain containing a specific disc {z : vertical bar z - a vertical bar < t(0)}, with z(0) being a repelling fixed point and f' (z(0)) > 1, or a rationally indifferent fixed point and f' (z(0)) = 1, respectively; As applications, new dynamical properties of parametric families of the most well-known maps, including exponential maps of the forms ae(zn) + be(-zn), hyperbolic maps of the forms lambda sinh z, and cosh z+lambda, trigonometricmaps of the forms lambda sin z, and lambda cos z, etc, are obtained. Moreover, a new map with wandering domains is constructed.
KeywordFatou set Julia set Entire map Symmetry Wandering domain
Indexed BySCI
Funding ProjectNSF of China[11688101]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000764557600001
Citation statistics
Document Type期刊论文
Corresponding AuthorWang, Yue-Fei
Affiliation1.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China
2.Shenzhen Univ, Sch Math & Stat, Shenzhen 518060, Peoples R China
3.Chinese Acad Sci, Inst Math, AMSS, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Cao, Chun-Lei,Wang, Yue-Fei. On the Dynamics of Entire Maps with Symmetry[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,2022:41.
APA Cao, Chun-Lei,&Wang, Yue-Fei.(2022).On the Dynamics of Entire Maps with Symmetry.JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,41.
MLA Cao, Chun-Lei,et al."On the Dynamics of Entire Maps with Symmetry".JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS (2022):41.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Cao, Chun-Lei]'s Articles
[Wang, Yue-Fei]'s Articles
Baidu academic
Similar articles in Baidu academic
[Cao, Chun-Lei]'s Articles
[Wang, Yue-Fei]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Cao, Chun-Lei]'s Articles
[Wang, Yue-Fei]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.