Iterates of Blaschke Products and Peano Curves
Iterates of Blaschke Products and Peano Curves
Abstract Let $f$ be a finite Blaschke product with $f(0)=0$, which is not a rotation and let $f^{n}$ be its $n$-th iterate. Given a sequence $\{a_{n}\}$ of complex numbers consider $F= \sum a_n f^{n}$. If $\{a_n\}$ tends to $0$ but $\sum |a_n| = \infty $, we prove that for any …