有理函数非一致双曲条件的共轭不变性

发布时间：2018-04-10 06:15

本文选题：有理函数　切入点：拓扑共轭　出处：《河南大学》2017年硕士论文

【摘要】：本论文主要研究有理函数非一致双曲条件的共轭不变性.我们知道,CE条件是常用的非一致双曲条件,在有多个临界点的情况下,CE条件不具有拓扑不变性.已有结果给出三种附加条件,并证明了对于多峰区间映射,CE条件加上附加条件之后具有共轭不变性.本文证明了对于有理函数,CE条件加上附加条件之后也具有共轭不变性.论文内容共分为三章.在第一章中,我们介绍了复解析动力系统的起源、发展和一些与本文相关的背景知识,并且介绍了本文用到的术语、记号和主要的研究成果.在第二章中,我们简要介绍了一些复分析和复解析动力系统中的基本概念和定理.在第三章中,我们主要证明了对于映射度至少为2的有理函数,CE条件附加上另外一些条件之后,在拓扑共轭下是不变的.相比已知结果,本文的工作证明了有理映射的情况,使我们对CE条件拓扑不变性的理解更加全面和深刻.
[Abstract]:In this paper, the conjugate invariance of nonuniformly hyperbolic conditions of rational functions is studied.We know that the CE condition is a commonly used nonuniform hyperbolic condition and has no topological invariance in the case of multiple critical points.Three additional conditions are given and it is proved that there is conjugate invariance for the CE condition with additional conditions for the multipeak interval mapping.In this paper, it is proved that there is also conjugate invariance for the CE condition of the rational function with additional conditions.The thesis is divided into three chapters.In the first chapter, we introduce the origin and development of complex analytic dynamical system and some background knowledge related to this paper, and introduce the terminology, notation and main research results used in this paper.In the second chapter, we briefly introduce some basic concepts and theorems in complex analysis and complex analytic dynamical systems.In chapter 3, we mainly prove that the CE condition is invariant under topological conjugation after attaching some other conditions to the CE condition of the rational function whose mapping degree is at least 2.Compared with the known results, this paper proves the case of rational mapping, which makes our understanding of the topological invariance of CE conditions more comprehensive and profound.
【学位授予单位】：河南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O19

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