复域差分与差分方程

　　《数学专著系列丛书：复域差分与差分方程》主要介绍近七年来复域差分，差分方程的研究成果，其中包括：亚纯函数Nevanlinna理论的差分模拟，如对数导数的差分模拟，Clunie引理的差分模拟，涉及差分的多项式值分布性质，以及亚纯函数涉及差分，移动的分担值问题。同时介绍复域差分方程的研究成果，包括线性差分方程与非线性差分方程的一般理论，几种典型的非线性差分方程，如差分Riccati方程，差分Painleve方程的解析理论。还将介绍q-差分的Nevanlinna理论的差分模拟，及q-差分方程的解析理论。以上内容主要来自近七年Halburd，Korhonen，Laine，C.C.Yang，Bergwerler，Ablowitz，Y.M.Chiang，S.J.Feng，作者本人及其团队关于复域差分，差分方程的研究文献。

暂缺《复域差分与差分方程》作者简介

Preface
List of Symbols
Chapter 1 Basic Properties of Complex Differences
　1.1 Preliminaries
　1.2 Difference Analogue of the Lemma on the Logarithmic Derivative
　1.3 Estimations of N(r, f(z + η)
　1.4 Estimations of T(r, f(z + η)
　1.5 Difference Analogue of the Clunie Lemma
　1.6 Difference Analogue of the Mohon'ko Lemma
　1.7 Difference Analogue of the Second Main Theorem
　1.8 Characteristic Functions of △nf
Chapter 2 Relationships Between Meromorphic Functions and Differences
　2.1 Relationships of f(z) and △nf(z)
　2.2 Fixed Points of f(z), f(z + c) and △f(z)
Chapter 3 Differences of Meromorphic Functions with Small Growth
　3.1 Divided Differences of Entire Functions of order < 1
　3.2 Differences of Entire Functions of order≤ 1
　3.3 Differences of Meromorphic Functions
　3.4 Second Differences of Meromorphic Functions with Small Growth
Chapter 4 Properties of Difference Polynomials
　4.1 Difference Analogues of f(z)nf'(z)
　4.2 Difference Analogues of f'(z) - af(z)
　4.3 Difference Analogue of the Tumura-Clunie Type Theorems
Chapter 5 Linear First Order Difference Equations
　5.1 Equations Concerning Gamma Function
　5.2 General Linear First Order Difference Equations
　5.3 Differences of Solutions for Difference Equations, and Differences of r(z)
Chapter 6 Linear Higher Order Difference Equations
　6.1 Difference Equations with Rational Coefficients
　6.2 Difference Equations with Transcendental Coefficients
Chapter 7 Basic Properties of Nonlinear Difference Equations
　7.1 Basic Properties Concerning Order Number
　7.2 Properties of Meromorphic Solutions
Chapter 8 Difference Riccati Equations
　8.1 Pielou Logistic Equation
　8.2 Difference Riccati Equations
　8.3 A Family of Solutions for Difference Riccati Equations
Chapter 9 Difference Painleve Equations
　9.1 Classified of Second Difference Equations
　9.2 Difference PainleveⅡ Equations
　9.3 Difference Painleve Ⅰ Equations
　9.4 Difference Painleve Ⅲ Equations
Chapter 10 Complex q-Differences and q-Difference Equations
　10.1 Properties of q-Differences
　10.2 Linear q-Difference Equations
　10.3 Non-Linear q-Difference Equations
　10.4 q-Difference Riceati equations
Chapter 11 Unicity of Meromorphic Functions Concerning Their Differences and Shifts
　11.1 Meromorphic Functions f(z) that Share Values with f(z + c)
　11.2 Meromorphic Functions f(z) that Share Values with △f(z)
　11.3 Meromorphic Functions f(z) that Share Values with △f(z) and△2/(z)
　11.4 Meromorphic Functions f(z) that Share Values with △nf(z)
Bibliography
Index