  A holomorphic endomorphism f of CP^2 admits a Julia set J_1, defined as usual
to be the locus of non-normality of its iterates, and a (typically) smaller
Julia set J_2, which is essentially the closure of the set of repelling
periodic orbits. The question has been raised whether J_1\J_2 is filled
(possibly in a measure-theoretic sense) with "Fatou subvarieties" along which
the dynamics is locally equicontinuous. In this article we construct examples
showing that this is not the case in general
