本文選題：Picard型定理 + 全純矩陣函數(shù)��； 參考：《北京郵電大學(xué)》2017年碩士論文

【摘要】：值分布和復(fù)動(dòng)力系統(tǒng)是復(fù)分析中兩個(gè)重要的研究方向。本文把亞純函數(shù)的動(dòng)力學(xué)性質(zhì)和值分布理論推廣到了一類全純矩陣函數(shù)上。首先,利用復(fù)分析和矩陣分析的相關(guān)知識(shí),我們研究了與整函數(shù)f相對(duì)應(yīng)的C2×2矩陣空間上的全純矩陣函數(shù)F的解析性質(zhì),給出了C2×2矩陣空間上全純矩陣函數(shù)的Picard型定理,同時(shí)得到了全純矩陣函數(shù)存在例外值的充分必要條件。利用整函數(shù)漸近值性質(zhì),建立了全純矩陣函數(shù)例外值與漸近值之間的聯(lián)系。我們還研究了全純矩陣函數(shù)周期點(diǎn)的性質(zhì),得到了相對(duì)應(yīng)的整函數(shù)f的Julia集的特征。進(jìn)一步,將C2×2矩陣空間的全純矩陣函數(shù)的相關(guān)性質(zhì)推廣到了一般高維矩陣函數(shù)上,得到了與整函數(shù)f相對(duì)應(yīng)的Cn×n矩陣空間上的全純矩陣函數(shù)F的解析性質(zhì)。
[Abstract]:The value distribution and the complex dynamic system are two important research directions in complex analysis. In this paper, the dynamic properties of meromorphic functions and the theory of value distribution are generalized to a class of holomorphic matrix functions. First, by using the related knowledge of complex analysis and matrix analysis, we have studied the Holomorphic matrix functions of the C2 x 2 matrix space corresponding to the whole function f. The Picard type theorem of the Holomorphic matrix function in the space of C2 x 2 matrix is given, and the necessary and sufficient conditions for the existence of the exceptional value of the Holomorphic matrix function are obtained. The connection between the exceptional value of the Holomorphic matrix function and the asymptotic value is established by using the asymptotic property of the whole function. We also study the periodic point of the Holomorphic matrix function. The properties of the Julia set of the corresponding integral function f are obtained. Further, the related properties of the Holomorphic matrix function of the C2 x 2 matrix space are generalized to the general high dimensional matrix function, and the solution properties of the Holomorphic matrix function F on the Cn * n matrix space corresponding to the whole function F are obtained.
【學(xué)位授予單位】：北京郵電大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O151.21;O174.52

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