Invariant escaping Fatou components with two rank-one limit functions for automorphisms of

We construct automorphisms of C² , and more precisely transcendental Hénon maps, with an invariant escaping Fatou component which has exactly two distinct limit functions, both of (generic) rank one. We also prove a general growth lemma for the norm of points in orbits belonging to invariant escaping Fatou components for automorphisms of the form $F(z,w)=(g(z,w),z)$ with g(z,w): C²→ C holomorphic.