發(fā)布時間：2018-04-10 06:15

  本文選題：有理函數(shù)　切入點：拓撲共軛　出處：《河南大學》2017年碩士論文

【摘要】：本論文主要研究有理函數(shù)非一致雙曲條件的共軛不變性.我們知道,CE條件是常用的非一致雙曲條件,在有多個臨界點的情況下,CE條件不具有拓撲不變性.已有結果給出三種附加條件,并證明了對于多峰區(qū)間映射,CE條件加上附加條件之后具有共軛不變性.本文證明了對于有理函數(shù),CE條件加上附加條件之后也具有共軛不變性.論文內容共分為三章.在第一章中,我們介紹了復解析動力系統(tǒng)的起源、發(fā)展和一些與本文相關的背景知識,并且介紹了本文用到的術語、記號和主要的研究成果.在第二章中,我們簡要介紹了一些復分析和復解析動力系統(tǒng)中的基本概念和定理.在第三章中,我們主要證明了對于映射度至少為2的有理函數(shù),CE條件附加上另外一些條件之后,在拓撲共軛下是不變的.相比已知結果,本文的工作證明了有理映射的情況,使我們對CE條件拓撲不變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.
【學位授予單位】：河南大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O19

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本文編號：1730018