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.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01925373
Contributeur : Johan Taflin <>
Soumis le : vendredi 16 novembre 2018 - 16:13:58
Dernière modification le : dimanche 18 novembre 2018 - 01:16:39

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fibered.pdf
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  • HAL Id : hal-01925373, version 1
  • ARXIV : 1811.06909

Citation

Christophe Dupont, Johan Taflin. Dynamics of fibered endomorphisms of $\mathbb P^k$. 2018. 〈hal-01925373〉

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