Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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F. Berteloot - F. Bianchi - C. Dupont

Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k)

created by stoppato on 03 Jul 2017
modified by bianchi on 11 Dec 2020


Published Paper

Inserted: 3 jul 2017
Last Updated: 11 dec 2020

Journal: Ann. Sci. Éc. Norm. Supér. (4)
Volume: 51
Year: 2018

ArXiv: 1403.7603 PDF
Links: arXiv


We introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of CP(k) and prove that it is equivalent to the stability of repelling cycles and equivalent to the existence of some measurable holomorphic motion of Julia sets which we call equilibrium lamination. We characterize the corresponding bifurcations by the strict subharmonicity of the sum of Lyapunov exponents or the instability of critical dynamics and analyze how repelling cycles may bifurcate. Our methods deeply exploit the properties of Lyapunov exponents and are based on ergodic theory and on pluripotential theory.

Tags: FIRB2012-DGGFT

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