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

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