Dynamics of fibered endomorphisms of \mathbb P^k

2018/11/16 by Dupont, Christophe, Taflin, Johan
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.06909

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 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.

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