An a priori bound of endomorphisms of $\mathbb{C}{\mathbb{P}}^k$ and a remark on the Makienko conjecture in dimension one

Yûsuke Okuyama

Let $f$ be an endomorphism of $\mathbb{C}{\mathbb{P}}^k$ of degree $>1$, and assume that for any cyclic Fatou component $W$ of $f$ having a period $p\in \mathbb{N}$, the equilibrium m…