On the Dynamics of Entire Maps with Symmetry

doi:10.1007/s10884-022-10144-3

CSpace

	On the Dynamics of Entire Maps with Symmetry
	Cao, Chun-Lei 1; Wang, Yue-Fei 2,3
	2022-03-04
发表期刊	JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
ISSN	1040-7294
页码	41
摘要	This 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.
关键词	Fatou set Julia set Entire map Symmetry Wandering domain
DOI	10.1007/s10884-022-10144-3
收录类别	SCI
语种	英语
资助项目	NSF of China[11688101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000764557600001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60089
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Yue-Fei
作者单位	1.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
推荐引用方式 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.