Consider the parameter space P[lamda] [SUBSET OF] C2 of complex H´ non maps e Hc,a ( x, y) = ( x2 + c + ay, ax), a 0 which have a fixed point with one eigenvalue a root of unity [lamda] = e2[pi]ip/q ; this is a parabola in a2 . Inside the parabola P[lamda] , we look at those H´ non maps that e are small perturbations of a quadratic polynomial p with a parabolic fixed point of multiplier [lamda]. We prove that there is an open disk of parameters (inside P[lamda] ) for which the semi-parabolic H´ non map is structurally stable on the Julia sets e J and J + . The set J + is homeomorphic to an inductive limit of J p x D under an 2 z appropriate solenoidal map [psi] : J p x D [RIGHTWARDS ARROW] J p x D, [psi]([zeta], z) = p([zeta] ), [zeta] [-] , where p ([zeta] ) J p is the Julia set of the polynomial p. The set J is homeomorphic to a solenoid with identifications, hence connected. We also consider the class of H´ non maps that are small perturbations of a e hyperbolic (or parabolic) polynomial p( x) = x2 + c. We describe the set J + as the quotient of 3-sphere with a dyadic solenoid removed by an equivalence relation. We define a lamination for the H´ non map by lifting the Thurston lamination e of the polynomial p from the closed unit disk to the unit 4-ball in C2 , using the inductive limit. "Lifting" the leaves of the lamination of the polynomial gives a lamination for the H´ non map. e