Abstract

Fibred holomorphic dynamics are skew-product transformations F(, z) = ( + α, f(z)) over an irrational rotation, such that f is holomorphic for every . In this paper we study such a dynamics in a neighbourhood of an invariant curve. We obtain some results analogous to the results in the non-fibred case. In particular, we prove a fibred version of the folklore result stating that Lyapounov stability is equivalent to linearization around a fixed point. We also obtain a fibred version of the Pérez-Marco continua. © 2007 IOP Publishing Ltd and London Mathematical Society.