Invariant graphs of rational maps

Guizhen Cui, Yan Gao, Jinsong Zeng

Published 2019-07-05Version 1

Let $f$ be a postcritically finite rational map. We prove that, as $n$ large enough, there exists an $f^n$-invariant (finite connected) graph on $\widehat{\mathbb{C}}$ such that it contains the postcritical set of $f$.