Extensions of Henon maps to the closed 4-ball

Any polynomial automorphism of C-2 with nontrivial dynamics is conjugate to a diffeomorphism of the 4-ball such that this diffeomorphism extends to a diffeomorphism of the closed 4-ball. Moreover, the conjugating map is a smo oth bijection of C-2 to itself. On the sphere at infinity, the extension ha s an attracting and a repelling solenoid, and the dynamics near these invar iant solenoids are described by conjugation to a model solenoidal map.