Abstract:

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 f and g with fixed points are topologically conjugate if and only if ρ(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.

Key words: topological conjugacy, holomorphic automorphism, unit disk, upper half plane, homeomorphism