Convergence of the iterates $\sum f^n$ of a non-rotation self-map of the disk fixing $0$

Assume \(f ( z )\) is analytic in D and \(f ( 0 ) = 0\) and is not a rotation \(( { \mathrm { i . e . ~ } } f ( z ) \neq e ^ { i \theta } z )\) . Show that \(\sum _ { n = 1 } ^ { \infty } f ^ { n } ( z )\) converges uniformly to an analytic function on compact subsets of D, where \(f ^ { n + 1 } ( z ) = f ( f ^ { n } ( z ) )\)