Sparsity of postcritically finite maps of ${\mathbb{P}}^k$ and beyond: A complex analytic approach

Thomas Gauthier, Johan Taflin, Gabriel Vigny

An endomorphism $f:{\mathbb{P}}^k\to {\mathbb{P}}^k$ of degree $d\ge 2$ is said to be postcritically finite (or PCF) if its critical set $\mathrm{Crit}(f)$ is preperiodic, i.e. if there…