Polynomial contractions of ${\mathbb{C}}^d$ and degree growth

Abstract

We give a simple example of a polynomial contraction automorphism of ${\mathbb{C}}^d$, $d\ge 3$, with unbounded degree growth. Combined with Poincaré-Dulac theorem it provides an algebraic automorphism of ${\mathbb{C}}^d$, $d\ge 3$, which is holomorphically but not algebraically linearizable.

4 pp. comments are welcome