Variation of Canonical Height for Fatou points on ${\mathbb{P}}^1$

Laura DeMarco, Niki Myrto Mavraki

Let $f:{\mathbb{P}}^1\to {\mathbb{P}}^1$ be a map of degree $>1$ defined over a function field $k=K(X)$, where $K$ is a number field and $X$ is a projective curve over $K$. For each…