Variation of the canonical height in a family of rational maps

Dragos Ghioca, Niki Myrto Mavraki

Let $d\ge 2$ be an integer, let $c(t)$ be any rational map, and let $f_t(z):=(z^d+t)/z$ be a family of rational maps indexed by t. For each algebraic number $t$, we let $h_{f_t}(…