Brody curves in complicated sets

Abstract

For a hyperbolic generalized Hénon mapping (in the sense of [3]), J + , the boundary of the set of non-escaping points, is known as a complicated set and also known to admit a foliation by biholomorphic images of C (see [3], [8]). We prove the existence of a leaf, which is injective Brody in P 2 , in the foliation of J + for certain Hénon mappings (for the definition of injective Brodyness, see Section 3).