Construction of Some Curious Diffeomorphisms of the Riemann Sphere
Construction of Some Curious Diffeomorphisms of the Riemann Sphere
复制标题
黎曼球的一些奇怪的微分同构的构造
DOI：
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发表时间：
1986
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通讯作者：
M. Herman
中科院分区：
文献类型：
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作者：
M. Herman
记法我们用§ 2表示黎曼球面C U {00}，对于a e U，我们用Ra：z >e 2nia z表示旋转数a的§ 2的旋转，固定点为0和00。在S 2 c W上，我们放置标准诱导度量d;对于f> 0，中心为x的f球为{ye § 2：d（x，y）<f}。在§ 2的子集上，我们放置诱导拓扑。给定A c= § 2，我们用= {ye §*：d（y，A）<e}表示A的e-邻域。我们用B = {zeC：|z| < 1}。如果我们写p/qeQ，我们将假设q ^ 1，并且p和q是互质的。
Notation We denote the Riemann sphere C U {00} by § 2 and for a e U, we denote by R a :z >e 2nia z the rotation of § 2 of rotation number a with fixed points 0 and 00. On S 2 c W we put the standard induced metric d; and for / > 0 the /-ball with centre x is {ye § 2 :d(x, y) < /}. On subsets of § 2 we put the induced topology. Given A c= § 2 we denote the e-neighbourhood of A by = {ye §*:d(y,A)<e}. We denote the unit disk by B = {zeC:|z|< 1}. If we write p/qeQ we shall suppose that q ^ 1, and p and q are relatively prime.