KMS Of Academy of mathematics and systems sciences, CAS
On the Dynamics of Entire Maps with Symmetry | |
Cao, Chun-Lei1; Wang, Yue-Fei2,3 | |
2022-03-04 | |
Source Publication | JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS |
ISSN | 1040-7294 |
Pages | 41 |
Abstract | 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. |
Keyword | Fatou set Julia set Entire map Symmetry Wandering domain |
DOI | 10.1007/s10884-022-10144-3 |
Indexed By | SCI |
Language | 英语 |
Funding Project | NSF of China[11688101] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000764557600001 |
Publisher | SPRINGER |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60089 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Wang, Yue-Fei |
Affiliation | 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 |
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. |
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