On the Dynamics of Nondegenerate Polynomial Endomorphisms of C2

We generalize the Brolin-Lyubich theorem for nondegenerate polynomial endomorphisms of C2. We prove, for a nondegenerate polynomial endomorphism p with the hyperbolic restriction to the line at infinity, that its canonical invariant current vp is a complex cycle near the line at infinity in the sense of Sullivan In¨ent. Math. 36 1976., 225]255..