單連通區(qū)域上全純自同構(gòu)的拓?fù)涔曹椃诸?/H1>
發(fā)布時(shí)間：2018-09-10 16:20
【摘要】：本文主要介紹了單連通區(qū)域上全純自同構(gòu)的拓?fù)涔曹椃诸?我們說(shuō)兩個(gè)變換f:X→X和g:Y→Y是拓?fù)涔曹椀?如果存在一個(gè)同胚h(yuǎn):X→Y使得h(?)f=g(?)h,這里(?)是映射的復(fù)合.單連通區(qū)域主要包括:復(fù)平面,擴(kuò)充復(fù)平面,單位圓盤和上半平面.關(guān)于復(fù)平面上全純自同構(gòu)的拓?fù)涔曹椃诸悊栴},Budnitska得到了更一般的結(jié)論,即有限維向量空間上仿射算子的拓?fù)涔曹椃诸?具體地講,如果仿射算子f(x)=Ax+b有一個(gè)不動(dòng)點(diǎn),那么f拓?fù)涔曹椨谒木�性部分A;如果仿射算子f:U→U無(wú)不動(dòng)點(diǎn),我們證明f拓?fù)涔曹椨谝粋�(gè)仿射算子g:U→U,這里U是g的不變子空間V和W的正交直和,g在V上的限制g|V是一個(gè)擁有如下形式的V的標(biāo)準(zhǔn)正交基底的仿射算子(x1,x2,...,xn)→(x1+1,x2,...,xn-1,εxn),ε=±1,它是由f唯一確定的,g在W上的限制g|W是一個(gè)通過(guò)冪零Jordan矩陣給出的W的標(biāo)準(zhǔn)正交基底的線性算子,是由f唯一確定的.對(duì)于擴(kuò)充復(fù)平面上的分式線性變換的拓?fù)涔曹椃诸悊栴},Rybalkina和S ergeichuk已經(jīng)給出了相應(yīng)的結(jié)果.我們?cè)诖苏聿⒖偨Y(jié)了復(fù)平面和擴(kuò)充復(fù)平面上全純自同構(gòu)的拓?fù)涔曹椃诸?關(guān)于單位圓盤和上半平面上全純自同構(gòu)的拓?fù)涔曹椫皼]有得到完全的分類,本文將就這一問題給出答案.我們通過(guò)旋轉(zhuǎn)理論及構(gòu)造同胚的方法,證明了:上半平面上(單位圓盤)所有無(wú)不動(dòng)點(diǎn)的全純自同構(gòu)之間都是拓?fù)涔曹椀?兩個(gè)有不動(dòng)點(diǎn)的全純自同構(gòu)f和g是拓?fù)涔曹椀漠?dāng)且僅當(dāng)ρ(f)=±ρ(g),modZ;無(wú)不動(dòng)點(diǎn)的全純自同構(gòu)與有不動(dòng)點(diǎn)的全純自同構(gòu)之間是不拓?fù)涔曹椀?
[Abstract]:In this paper, the topological conjugate classification of Holomorphic automorphism on a simple connected domain is introduced. We say that the two transformations f: X X and g: y y are topological conjugate, if there is a homomorphism h: X y such that h (?) FG (?) h, here (?) Is a composite of maps. Simple connected regions mainly include: complex plane, extended complex plane, unit disk and upper half plane. On topological conjugate classification of Holomorphic automorphism on complex plane Budnitska obtained a more general conclusion that is topological conjugate classification of affine operators on finite dimensional vector space. In particular, if the affine operator f (x) n Ax b has a fixed point, then f topology conjugates to its linear part A, and if the affine operator f: U U U has no fixed point, We prove that f topology is conjugate to an affine operator g: U, where U is the orthogonal direct sum of the invariant subspace V and W of g on V, g V is an affine operator with a standard orthonormal base of V in the following form. N (x 11 1 + x 2n 1, 蔚 xn), 蔚 = 鹵1), which is the limit g W on W determined only by f is a linear operator of the standard orthogonal base of W given by nilpotent Jordan matrix. Is determined only by f. For topological conjugate classification of fractional linear transformations on extended complex plane, the corresponding results have been given for Rybalkina and S ergeichuk. The topological conjugate classification of Holomorphic automorphism on complex plane and extended complex plane is summarized. The topological conjugate of Holomorphic automorphism on unit disk and upper half plane has not been completely classified before. This article will give the answer to this question. By means of rotation theory and the method of constructing homeomorphism, we prove that all Holomorphic automorphisms without fixed points on the upper half plane (unit disk) are topological conjugate; Two Holomorphic automorphisms f and g with fixed points are topological conjugate if and only if 蟻 (f) = 鹵蟻 (g) mod Z, and between Holomorphic automorphism without fixed point and Holomorphic automorphism with fixed point is not topological conjugate.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O189.11
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1 鄒成;;關(guān)于二次函數(shù)的拓?fù)涔曹梉J];甘肅聯(lián)合大學(xué)學(xué)報(bào)(自然科學(xué)版);2007年01期
2 代莉;;擬移位映射與移位映射拓?fù)涔曹梉J];懷化學(xué)院學(xué)報(bào);2009年02期
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1 潘嘯天;低維緊致連通李群上平移作用的拓?fù)涔曹椃诸怺D];吉林大學(xué);2015年
2 常偉;單連通區(qū)域上全純自同構(gòu)的拓?fù)涔曹椃诸怺D];吉林大學(xué);2017年
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，
本文編號(hào)：2234970
本文鏈接：http://sikaile.net/shoufeilunwen/benkebiyelunwen/2234970.html
[Abstract]:In this paper, the topological conjugate classification of Holomorphic automorphism on a simple connected domain is introduced. We say that the two transformations f: X X and g: y y are topological conjugate, if there is a homomorphism h: X y such that h (?) FG (?) h, here (?) Is a composite of maps. Simple connected regions mainly include: complex plane, extended complex plane, unit disk and upper half plane. On topological conjugate classification of Holomorphic automorphism on complex plane Budnitska obtained a more general conclusion that is topological conjugate classification of affine operators on finite dimensional vector space. In particular, if the affine operator f (x) n Ax b has a fixed point, then f topology conjugates to its linear part A, and if the affine operator f: U U U has no fixed point, We prove that f topology is conjugate to an affine operator g: U, where U is the orthogonal direct sum of the invariant subspace V and W of g on V, g V is an affine operator with a standard orthonormal base of V in the following form. N (x 11 1 + x 2n 1, 蔚 xn), 蔚 = 鹵1), which is the limit g W on W determined only by f is a linear operator of the standard orthogonal base of W given by nilpotent Jordan matrix. Is determined only by f. For topological conjugate classification of fractional linear transformations on extended complex plane, the corresponding results have been given for Rybalkina and S ergeichuk. The topological conjugate classification of Holomorphic automorphism on complex plane and extended complex plane is summarized. The topological conjugate of Holomorphic automorphism on unit disk and upper half plane has not been completely classified before. This article will give the answer to this question. By means of rotation theory and the method of constructing homeomorphism, we prove that all Holomorphic automorphisms without fixed points on the upper half plane (unit disk) are topological conjugate; Two Holomorphic automorphisms f and g with fixed points are topological conjugate if and only if 蟻 (f) = 鹵蟻 (g) mod Z, and between Holomorphic automorphism without fixed point and Holomorphic automorphism with fixed point is not topological conjugate.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O189.11
【相似文獻(xiàn)】
相關(guān)期刊論文 前10條
1 鄒成;;關(guān)于二次函數(shù)的拓?fù)涔曹梉J];甘肅聯(lián)合大學(xué)學(xué)報(bào)(自然科學(xué)版);2007年01期
2 代莉;;擬移位映射與移位映射拓?fù)涔曹梉J];懷化學(xué)院學(xué)報(bào);2009年02期
3 吳慶初;劉華祥;曾廣洪;;帳篷映射的幾何構(gòu)造方法[J];江西師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2006年02期
4 劉喜玲;;拓?fù)淇臻g中的拓?fù)涔曹椩诘械倪\(yùn)用[J];河南科技學(xué)院學(xué)報(bào)(自然科學(xué)版);2007年01期
5 張瑩;;弱遍歷自同胚映射拓?fù)涔曹椀牡葍r(jià)條件[J];天津師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2008年02期
6 張無(wú)畏;一種區(qū)間映射混沌集的構(gòu)造[J];華東師范大學(xué)學(xué)報(bào)(自然科學(xué)版);1999年01期
7 劉俊鵬;;關(guān)于初值敏感依賴性在拓?fù)涔曹椣卤３值淖C明[J];洛陽(yáng)師范學(xué)院學(xué)報(bào);2012年11期
8 陳鳳娟;雙邊符號(hào)空間上的一類擬移位映射[J];浙江師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2004年01期
9 李自來(lái);王延庚;衛(wèi)國(guó);;加法機(jī)器拓?fù)涔曹椙度氲酵負(fù)鋭?dòng)力系統(tǒng)中的充要條件[J];西北大學(xué)學(xué)報(bào)(自然科學(xué)版);2011年05期
10 王立娟;廖公夫;;3階Feigenbaum映射的拓?fù)涔曹椥訹J];數(shù)學(xué)學(xué)報(bào);2006年04期
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1 潘嘯天;低維緊致連通李群上平移作用的拓?fù)涔曹椃诸怺D];吉林大學(xué);2015年
2 常偉;單連通區(qū)域上全純自同構(gòu)的拓?fù)涔曹椃诸怺D];吉林大學(xué);2017年
3 馮上期;Rule 57的拓?fù)鋭?dòng)力性質(zhì)的研究[D];華南理工大學(xué);2011年
4 毛靜麗;符號(hào)空間的理論[D];華中師范大學(xué);2012年
，本文編號(hào)：2234970
本文鏈接：http://sikaile.net/shoufeilunwen/benkebiyelunwen/2234970.html
