Automorphisms of complex surfaces can have various invariant curves. We consider rational surface automorphisms with invariant cubic curve, which have, at the same time, an invariant line, or an invariant quadratic curve, disjoint from the invariant cubic curve.
Some of them appear to have rotation domains of rank two, with two fixed points.
We prove that these fixed points are linearizable to irrational rotations.

(Additional talk as a short communication)
Title: Herman rings for Henon dynamics
Abstract : Recent numerical observations about Herman rings for Henon maps will be reported.