Berkovich space dynamics

Summary

Berkovich space dynamics studies the iteration of a rational map over a complete non-Archimedean field on the Berkovich projective line. More generally, it studies endomorphisms of Berkovich analytic spaces. The field itself, such as $\C_p$, is totally disconnected and not locally compact, which makes analysis of orbits awkward. The Berkovich projective line adds extra points to $\mathbb{P}^1(\C_p)$ and is compact, Hausdorff and path-connected. Every rational map extends to it continuously. On this space one gets Julia sets, Fatou sets and invariant measures that behave much like those of complex dynamics.