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Dynamics of fibered endomorphisms of $\mathbb P^k$ (1811.06909v1)
Published 16 Nov 2018 in math.CV and math.DS
Abstract: We study the structure and the Lyapunov exponents of the equilibrium measure of endomorphisms of $\mathbb Pk$ preserving a fibration. We extend the decomposition of the equilibrium measure obtained by Jonsson for polynomial skew products of $\mathbb C2$. 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.