Compact composition operators and iteration
Let $\Omega$ be a domain in the complex plane, $\phi$ an analytic map that maps $\Omega$ into itself, and $X$ an $F$-space of analytic functions in $\Omega$ that possesses certain mild regularity properties. (Some examples considered in the paper are Hardy spaces, Bergman spaces, and the space of all analytic functions in $\Omega$.) If composition with $\phi$ defines a compact operator on $X$ that
