Sums of Lyapunov exponents for some polynomial maps of ${\bf C}^2$

Abstract

We give a formula for the sum of the Lyapunov exponents of a nondegenerate polynomial map $f$ of ${\bf C}^{2}$ close to $(z,w)\to (z^d,w^d)$. The formula only involves the behavior of $f$ at infinity. In particular, it follows that the sum only depends on the homogeneous part of $f$ of degree $d$.