复域差分与差分方程

PrefaceList of SymbolsChapter 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 △nfChapter 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 GrowthChapter 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 TheoremsChapter 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 CoefficientsChapter 7 Basic Properties of Nonlinear Difference Equations　7.1 Basic Properties Concerning Order Number　7.2 Properties of Meromorphic SolutionsChapter 8 Difference Riccati Equations　8.1 Pielou Logistic Equation　8.2 Difference Riccati Equations　8.3 A Family of Solutions for Difference Riccati EquationsChapter 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 EquationsChapter 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 equationsChapter 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)BibliographyIndex

《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。