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Discrete functional equations in complex domains

复杂域中的离散函数方程

基本信息

批准号：
16540202
负责人：
ISHIZAKI Katsuya
金额：
$ 2.11万
依托单位：
Nippon Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540202/
关键词：
Difference equations q-difference equations The Schroeder equation Nevanlinna theory Complex dynamics Uniqueness theory Algebroid functions The Painleve equation Schr"oder方程式 Painlev'e方程式

项目摘要

By means of the value distribution theory, we investigated ordinary differential equations and discrete functional equations in complex domains, in particular, linear difference equations having polynomial coefficients and the Schroeder functional equations. We obtain results on Malmquist-Yoshida type theorems for nonlinear differential equations in connection with complex dynamics theory, and results on linear differential equation of the second order with elliptic coefficients. We also constructed Wiman-Valiron theory for binomial series in order to treat linear difference equations. The Schroeder equations are considered from the point of view of the connections between the Nevanlinna theory and the complex dynamics theory. In particular, we gave a proof of the result on Borel directions of the Schroeder functions and the Julia set of the rational functions from which the Schroeder functions are generated. Below we report the researches by each investigator.Mori obtained uniqueness … More theorems on some complex domains which are bounded or countable.Shimomura investigated Painleve transcendents. He obtained the lower estimate on meromorphic solutions of higher order Painleve equations. Modified type of Painleve equations (III), and (V) are considered. He also gave nontrivial examples on nonlinear differential equations having the Painleve properties.Morosawa considered the parameter space of complex dynamics on the complex error functions. He obtained the topological properties of the Julia set of the hyperbolic complex error function.Fermat type functional equations are treated by Tohge. With Professor Gundersen (New Orleans), he found a new entire function satisfying a Fermat type equation. He also investigated the value distribution theory in angular domains.Sawada obtained an algebroid function with three sheets on which analytic functions have deficiencies restricted by some given conditions. He also treated meromorphic solutions of some algebraic differential equations. Less

借助于值分布理论，我们研究了复域上的常微分方程组和离散泛函方程，特别是具有多项式系数的线性差分方程和Schroeder泛函方程。结合复动力学理论，得到了非线性微分方程解的Malmquist-Yoshida型定理和二阶线性椭圆型微分方程解的结果。为了处理线性差分方程组，我们还构造了二项级数的Wiman-Valron理论。从Niganlinna理论和复动力学理论之间的联系的角度考虑了Schroeder方程。特别地，我们证明了Schroeder函数的Borel方向和生成Schroeder函数的有理函数的Julia集的结果。下面我们报告每个研究人员的研究。Mori获得唯一性…关于某些有界或可数复域的更多定理。下村研究了Painleve超越。得到了高阶Painleve方程亚纯解的下界估计。考虑了改进型Painleve方程(III)和(V)。他还给出了具有Painleve性质的非线性微分方程的非平凡例子。Morosawa考虑了复误差函数上的复动力学参数空间。他得到了双曲复误差函数的Julia集的拓扑性质，并用Tohge处理了Fermat型函数方程。与甘德森教授(新奥尔良)一起，他发现了一个新的满足费马型方程的整函数。他还研究了角域中的值分布理论。Sawada得到了一个三叶代数体函数，该函数上的解析函数在一定条件下具有亏损性。他还研究了一些代数微分方程亚纯解。较少