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meromorphic iterative roots of linear fractional functions

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Science China Mathematics 2009年第5期52卷 941-948页

作者： SHI YongGuo CHEN Li Department of Mathematics Sichuan UniversityChengdu 610064China Key Laboratory of Numerical Simulation of Sichuan Province and College of Mathematics and Information Science Neijiang Normal UniversityNeijiang 641112China

Iterative root problem can be regarded as a weak version of the problem of embedding a homeomorphism into a flow. There are many results on iterative roots of monotone functions. However, this problem gets more difficult in non-monotone cases. Therefore, it is interesting to find iterative roots of linear fractional functions (abbreviated as LFFs), a class of non-monotone functions on R. In this paper, iterative roots of LFFs are studied on C. An equivalence between the iterative functional equation for non-constant LFFs and the matrix equation is given. By means of a method of finding matrix roots, general formulae of all meromorphic iterative roots of LFFs are obtained and the precise number of roots is also determined in various cases. As applications, we present all meromorphic iterative roots for functions z and 1/z.

关键词： iterative functional equation linear fractional function meromorphic solution ma- trix equation

On a certain classes of meromorphic functions with positive coefficients

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Applied Mathematics(A Journal of Chinese Universities) 2019年第3期34卷 253-260页

作者： R.Asadi A.Ebadian S.Shams Janusz Sokol Department of Mathematics Faculty of ScienceUrmia UniversityUrmiaIran

In this paper certain classes of meromorphic functions in punctured unit disk are defined.Some properties including coefficient inequalities,convolution and other results are investigated.

关键词： Hadamard product univalent meromorphic functions

Normal families of meromorphic mappings of several complex variables into P^(N)(C) for moving targets

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Science China Mathematics 2005年第Z1期48卷 355-364页

作者： TU Zhenhan LI Pingli School of Mathematics and Statistics Wuhan UniversityWuhan430072China School of Mathematics and StatisticsWuhan UniversityWuhan430072China

Motivated by Ru and Stoll's accomplishment of the second main theorem in higher dimension with moving targets, many authors studied the moving target problems in value distribution theory and related topics. But thereafter up to the present, all of researches about normality criteria for families of meromorphic mappings of several complex variables into PN(C) have been still restricted to the hyperplane case. In this paper, we prove some normality criteria for families of meromorphic mappings of several complex variables into PN(C) for moving hyperplanes, related to Nochka's Picard-type theorems.The new normality criteria greatly extend earlier related results.

关键词： complex projective spaces, meromorphic mappings, moving targets, normal families and value distribution theory.

Degeneracy and Finiteness Theorems for meromorphic Mappings in Several Complex Variables

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Chinese Annals of Mathematics,Series B 2019年第2期40卷 251-272页

作者： Si Duc QUANG Department of Mathematics Hanoi National University of Education Thang Long Institute of Mathematics and Applied Sciences

The author proves that there are at most two meromorphic mappings of C^m into P^n(C)(n ≥ 2) sharing 2 n+ 2 hyperplanes in general position regardless of multiplicity,where all zeros with multiplicities more than certain values do not need to be counted. He also shows that if three meromorphic mappings f^1, f^2, f^3 of Cminto P^n(C)(n ≥ 5) share2 n+1 hyperplanes in general position with truncated multiplicity, then the map f^1×f^2×f^3 is linearly degenerate.

关键词： Second main theorem Uniqueness problem meromorphic mapping Multiplicity

Equidistribution for meromorphic transforms and the dd^c-method

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Science China Mathematics 2005年第Z1期48卷 180-194页

作者： Tien-Cuong Dinh Nessim Sibony Mathématique-Bt.425 UMR 8628 Université Paris-Sud91405 OrsayFranceMathématique-Bt.425 UMR 8628Université Paris-Sud91405 OrsayFrance

In this paper we give an introduction to the notion of meromorphic transform.We describe some equidistribution problems and their solution, using the ddc-method. In particular, we give some statistical properties of the equilibrium measure for meromorphic maps on compact Kahler manifolds: K-mixing, exponential decay of correlations and central limit theorem.

关键词： meromorphic map, correspondence, compact Kahler manifold.

Some remarks on the genericity of unique range sets for meromorphic functions

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Science China Mathematics 2005年第Z1期48卷 262-267页

作者： Ha Huy Khoai Institute of Mathematics 18 Hoang Quoc Viet 10307HanoiVietnam

In this paper we relate the study of unique range sets for meromorphic functions (URSM) with the hyperbolic hypersurfaces and give some remarks on the genericity of unique range sets for meromorphic functions.

关键词： unique range set for meromorphic functions, hyperbolic surface.

On transcendental meromorphic functions with radially distributed values

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Science China Mathematics 2004年第3期47卷 401-416页

作者： ZHENG Jianhua Department of Mathematical Sciences Tsinghua University Beijing 100084 China

The growth of transcendental meromorphic functions in terms of their orders is investigated in this paper when they and their derivatives have radially distributed values following the discussion of the author . A simple andelementary way to study such subjects is exhibited in this paper; that is,once an estimation of B(r,*) in terms of a few C(r,**) in the Nevanlinna theory on angular domains is established, we can produce one result that the order of a mermorphic function with radially distributed values related to C(r,**) can be estimated under the assumption of existence of suitable deficient value. The results obtained in this paper lead us to a new singular direction in terms of Nevanlinna characterstic instead of the order of meromorphic functions.

关键词： Nevanlinna theory, meromorphic function and radial distribution.

VALUE DISTRIBUTION OF meromorphic SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS

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Acta Mathematica Scientia 2019年第4期39卷 1173-1184页

作者：陈敏风高宗升张继龙 School of Mathematics and Statistics Guangdong University of Foreign Studies Guangzhou 510006 China LMIB and School of Mathematics and Systems Science Beihang University Beijing 100191 China

In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.

关键词： Non-linear difference equation meromorphic solution rational solution value dist ribution

The uniqueness of meromorphic functions concerning small functions

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Science China Mathematics 2000年第6期43卷 581-590页

作者：李玉华乔建永 Center of Mathematics China University of Mining & Technology Beijing 100083

We prove that the Nevanlinna five-point-theorem on the uniqueness of meromorphic func-tions is valid for five small meromorphic functions.

关键词： meromorphic function small function uniqueness.