Polynomial proper maps between balls (Q1110691)

The author investigates the structure of polynomial proper maps between balls in (perhaps) different dimensional complex vector spaces. He verifies that for each odd positive integer there is a monomial proper map that is invariant under a certain matrix group. This result involves the invariance of monomial maps under finite unitary groups. As second he verifies that a proper holomorphic map between balls that is sufficiently regular at the boundary must admit a finite factorization that plays the role of a finite Blaschke product in one variable, and as a consequence must be rational.