Dynamics of polynomial automorphisms of \(\mathbb C^k\) (Q1426908)

The dynamics of polynomial automorphisms of \({\mathbb C}^2\) has been studied quite intensively in the past decade. Much less is known in the study of the dynamics of polynomial automorphisms of \({\mathbb C^k}, k\geq 3\). In this paper the dynamics of polynomial automorphisms of \({\mathbb C}^k\) is treated in detail. To an algebraically stable automorphism \(f\) positive closed currents which are invariant under \(f\) are associated, considering \(f\) as a rational map on \({\mathbf P}^k\). These currents give information on the dynamics and yield a canonical invariant measure which is shown to be mixing.