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

Christophe Dupont; Johan Taflin

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arXiv · 1811.06909

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

Christophe Dupont·Johan Taflin

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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.

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Christophe Dupont, Johan Taflin. 2018-11-16. Dynamics of fibered endomorphisms of $\mathbb P^k$. https://arxiv.org/abs/1811.06909

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