期刊：
Journal of Computational and Applied Mathematics,2020年368:112549 ISSN：0377-0427
通讯作者：
Ponnusamy, Saminathan
作者机构：
[Liu, Gang] Hengyang Normal Univ, Coll Math & Stat, Hunan Prov Key Lab Intelligent Informat Proc & Ap, Hengyang 421002, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] I;Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.
关键词：
Konig's method;Steffensen's method;Cycle;Attracting basin;Parabolic basin;Siegel disk
摘要：
The aim of this paper is to reveal some complex dynamical properties of Konig's and Steffensen's methods for entire functions. Two procedures are presented for constructing infinite entire functions simultaneously so that any given finite pairs of prescribed cycles occur when the two methods are applied, respectively. Furthermore, these functions can be chosen by polynomials or transcendental entire functions. (C) 2019 Elsevier B.V. All rights reserved.
作者机构：
[Liu, Gang] Hengyang Normal Univ, Coll Math & Stat, Hunan Prov Key Lab Intelligent Informat Proc & Ap, Hengyang 421002, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] I;Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India.
关键词：
Uniformly locally univalent;Analytic functions;Harmonic and stable harmonic mappings;Pre-Schwarzian and Schwarzian;Uniformly hyperbolic radius;Distortion;Hardy space;Bloch space;BMOA;BMOH;Subordination
摘要：
In this paper, we consider the class of uniformly locally univalent harmonic mappings in the unit disk and build a relationship between its pre-Schwarzian norm and uniformly hyperbolic radius. Also, we establish eight ways of characterizing uniformly locally univalent sense-preserving harmonic mappings. We also present some sharp distortions and growth estimates and investigate their connections with Hardy spaces. Finally, we study subordination principles of norm estimates. (C) 2017 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
期刊：
Journal of Computational and Applied Mathematics,2018年336:468-476 ISSN：0377-0427
通讯作者：
Ponnusamy, Saminathan
作者机构：
[Liu, Gang] Hengyang Normal Univ, Coll Math & Stat, Hunan Prov Key Lab Intelligent Informat Proc & Ap, Hengyang 421002, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Madras 600036, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] I;Indian Inst Technol Madras, Dept Math, Madras 600036, Tamil Nadu, India.
关键词：
König’s method;Cycle;Fatou set;Attracting basin;Parabolic basin;Siegel disk
摘要：
We consider König’s method for finding roots of polynomials. Let Kf,n be the function defined in König’s method for polynomial f of order n (n≥2). For any given complex number λ∈C and any given set Ω≔{z1,z2,…,zk} of k (k≥2) distinct complex numbers, we present a procedure of constructing a polynomial fn,λ for which Ω is a k-cycle of Kfn,λ,n with multiplier λ.
摘要：
The aim of this paper is twofold. One of them is to introduce the class of harmonic
$$\nu $$
-Bloch-type mappings as a generalization of harmonic
$$\nu $$
-Bloch mappings and thereby we generalize some recent results of harmonic 1-Bloch-type mappings investigated recently by Efraimidis et al. (Complex Var Elliptic Equ 62:1081–1092, 2017). The other is to investigate some subordination principles for harmonic Bloch mappings and then establish Bohr’s theorem for these mappings and in a general setting, in some cases.
作者机构：
[Liu, Gang] Hengyang Normal Univ, Coll Math & Stat, Hunan Prov Key Lab Intelligent Informat Proc & Ap, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Madras 600036, Tamil Nadu, India.;[Ponnusamy, Saminathan] IST, Chennai Ctr, 110 Nelson Manickam Rd, Madras 600029, Tamil Nadu, India.
通讯机构：
[Liu, Gang] H;Hengyang Normal Univ, Coll Math & Stat, Hunan Prov Key Lab Intelligent Informat Proc & Ap, Hengyang 421008, Hunan, Peoples R China.
会议名称：
7th International Conference on Complex Analysis and Dynamical Systems (CA&DS VII)
会议时间：
MAY 10-15, 2015
会议地点：
Nahariya, ISRAEL
会议主办单位：
[Liu, Gang] Hengyang Normal Univ, Coll Math & Stat, Hunan Prov Key Lab Intelligent Informat Proc & Ap, Hengyang 421008, Hunan, Peoples R China.^[Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Madras 600036, Tamil Nadu, India.^[Ponnusamy, Saminathan] IST, Chennai Ctr, 110 Nelson Manickam Rd, Madras 600029, Tamil Nadu, India.
会议论文集名称：
Contemporary Mathematics
关键词：
Analytic;anti-analytic;harmonic;biharmonic;p-harmonic;polyharmonic and composition
摘要：
The paper is devoted to the study of compositions of polyharmonic mappings in simply connected domains. More precisely, we determine necessary and sufficient conditions of polyharmonic mapping $f$ such that $f\circ F$ (resp. $F\circ f$) is $l$-harmonic for any analytic function (or harmonic mapping but not analytic, or $q$-harmonic mapping but not $(q-1)$-harmonic) $F$.
作者机构：
衡阳师范学院数学与统计学院, 衡阳, 421008;Indian Statistical Institute(ISI),Chennai Centre, India, Chennai, 600113;[陈少林; 刘刚] 衡阳师范学院数学与统计学院, 衡阳, 421008;[Saminathan Ponnusamy] Indian Statistical Institute(ISI),Chennai Centre, India, Chennai, 600113
期刊：
Journal of Mathematical Analysis and Applications,2015年432(1):356-366 ISSN：0022-247X
通讯作者：
Liu, Gang
作者机构：
[Liu, Gang] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.;[Gao, Junyang] China Univ Min & Technol Beijing, Sch Sci, Beijing 100083, Peoples R China.
通讯机构：
[Liu, Gang] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.
关键词：
Julia set;Konig's methods;Group of symmetries
摘要：
Let Sigma(R) be the group of symmetries of the Julia set of a rational map R and K-f,K-n be the Konig's method for polynomial f of order n (>= 2). For any given integer n >= 2, we prove that if f is in normal form, then Sigma(f) is a subgroup of Sigma(K-f,K-n). We also obtain a necessary and sufficient condition for the Julia set of K-f,K-n to be a line. (C) 2015 Elsevier Inc. All rights reserved.
