Equilibrium states of endomorphisms of ${\mathbb{P}}^k$ I: existence and properties

Fabrizio Bianchi, Tien-Cuong Dinh

We develop a new method, based on pluripotential theory, to study the transfer (Perron-Frobenius) operator induced on ${\mathbb{P}}^k={\mathbb{P}}^k(\mathbb{C})$ by a holomorphic endom…