Holomorphic dynamics in several variables

Summary

Holomorphic dynamics in several variables studies the iteration of holomorphic maps $f \colon X \to X$ of a complex manifold $X$ of dimension at least $2$. The two main families of examples are holomorphic endomorphisms of complex projective space $\mathbb{P}^k$ and polynomial automorphisms of $\C^2$, such as the Hénon maps. As in one-variable complex dynamics, space splits into a Fatou set, where the dynamics is stable, and a Julia set, where it is chaotic. Many tools are new, notably plurisubharmonic functions, positive closed currents and invariant measures.