Dynamics of fibered endomorphisms of ${\mathbb{P}}^k$

Abstract

We study the structure and the Lyapunov exponents of the equilibrium measure of endomorphisms of ${\mathbb{P}}^k$ preserving a fibration. We extend the decomposition of the equilibrium measure obtained by Jonsson for polynomial skew products of ${\mathbb{C}}^2$. We also show that the sum of the sectional exponents satisfies a Bedford-Jonsson formula when the fibration is linear, and that this function is plurisubharmonic on families of fibered endomorphisms. In particular, the sectional part of the bifurcation current is a closed positive current on the parameter space.