单位圆盘与上半平面上全纯自同构的拓扑共轭分类

Topologically Conjugate Classifications for Holomorphic Automorphisms on Unit Disk and Upper Half Plane

考虑单位圆盘与上半平面上全纯自同构的拓扑共轭分类,通过旋转理论及构造同胚,证明了:上半平面上所有无不动点的全纯自同构之间都是拓扑共轭的;两个有不动点的全纯自同构f和g拓扑共轭当且仅当ρ(f)=±ρ(g),mod Z;无不动点的全纯自同构与有不动点的全纯自同构之间是不拓扑共轭的.

The topologically conjugate classifications for holomorphic automorphisms on unit disk and upper half plane were considered.By rotation theory and some constructions of homeomorphisms,we prove that all holomorphic automorphisms on upper half plane without fixed points are topologically conjugate;two holomorphic automorphisms fand g with fixed points are topologically conjugate if and only ifρ（f）= ±ρ（g）,mod Z;a holomorphic automorphisms without fixed points and a holomorphic automorphisms with fixed points on upper half plane are not topologically conjugate.