Studies on complex dynamics of transcendental entire functions

超越整体函数的复杂动力学研究

基本信息

批准号：
17540163
负责人：
MOROSAWA Shunsuke
金额：
$ 1.86万
依托单位：
KOCHI UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17540163/
关键词：
complex dynamics transcendental entire function complex error function structurally finite entire singular value parameter space function hyperbolic component semihyperbolicity ファトウ集合ジュリア集合双曲型整関数

项目摘要

The summary of research results is as follows.1. Morosawa considers dynamics of complex error functions. In particular, he studies the parameter space of those functions with real coefficients. He obtains results on parabolic bifurcations along boundaries of hyperbolic components in the parameter space.2. Complex error functions belong to the family of the structurally finite entire functions, which is defined by Taniguchi. Structurally finite entire functions with two singular values are classified into three types; complex error functions, simply decorated exponential maps and cubic polynomials. Morosawa and Taniguchi study the hyperbolic components in the parameter space of structurally finite entire functions with two singular values. They obtain results on hyperbolic component of capture type and prepare a paper.3. Taniguchi considers covering structure of rational functions and entire functions and those dynamical structure and studies those relationships. He also gives a model of asymptotic Teichimiiller space.4. Tohge improves the condition on the uniqueness theorem of meromorphic functions defined in the plane. In particular, he obtains a result on a relations of two functions which comes from conditions on angular domains.5. Kisaka constructs transcendental entire functions with doubly connected wandering domain and, more generally, those with n-multiply connected wandering domains by using improved quasiconformal surgery. He also gives a characterization on semihyperbolicity of transcendental entire functions by using orbits of singular values.8. Ishizaki studies a relation ship between properties on solutions of the Schroder equations in value distribution theory and in theory of complex dynamics.

研究结果的摘要如下1。 Morosawa考虑了复杂误差函数的动力学。特别是，他研究了具有实际系数的这些功能的参数空间。他获得了沿参数空间中双曲线分量边界的抛物线分叉的结果。2。复杂的误差函数属于结构有限的整个功能的家族，该功能由Taniguchi定义。结构有限的整个功能具有两个单数值，分为三种类型。复杂的误差函数，简单地装饰了指数图和立方多项式。 Morosawa和Taniguchi研究了整个函数的参数空间中的双曲分量，具有两个奇异值。他们在捕获类型的双曲分量上获得结果。3。 Taniguchi认为涵盖了理性功能和整个功能的结构以及那些动态的结构和研究这些关系。他还提供了渐近teichimiiller空间的模型4。 Tohge改善了平面中定义的Meromorormormormormormormormormorthic函数的唯一性定理的条件。特别是，他获得了由角域上的条件产生的两个函数的关系的结果。5。基萨卡（Kisaka）通过使用改进的准文献手术进行双重连接的域构建整个功能，并更普遍地是具有N-多层连接的流浪结构域的整个功能。他还通过使用奇异值的轨道8。 Ishizaki研究了价值分布理论和复杂动力学理论中的schroder方程解决方案解决方案的属性之间的关系。