Filled Julia set of some class of Hénon-like map

Abstract

In this work we consider a class of endomorphisms of R 2 defined by f (x, y) = (xy + c, x), where c ∈ R is a real number and we prove that when −1 < c < 0, the forward filled Julia set of f is the union of stable manifolds of fixed and 3−periodic points of f . We also prove that the backward filled Julia set of f is the union of unstable manifolds of the saddle fixed and 3−periodic points of f .