- #1
henry1964
- 2
- 0
D is be a bounded domain in the complex plane. Suppose f : D -->D is a holomorphic automorphism (conformal bijection). Now define f_n(z) = f(f(f(f ..(z) (composed n times ).
Trying (and failing) to show:
(i) the sequence {f_n} has a subsequence that converges either to a constant
or to an automorphism of D
also
(ii) If the whole sequence {f_n} converges to g, then f(z)= z identically. $f(z)\equiv z
Trying (and failing) to show:
(i) the sequence {f_n} has a subsequence that converges either to a constant
or to an automorphism of D
also
(ii) If the whole sequence {f_n} converges to g, then f(z)= z identically. $f(z)\equiv z