Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CPkReportar como inadecuado




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* Corresponding author 1 IMT - Institut de Mathématiques de Toulouse UMR5219 2 IRMAR - Institut de Recherche Mathématique de Rennes

Abstract : We introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of CPk 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.

Keywords : holomorphic dynamics dynamical stability positive currents Lyapunov exponents





Autor: François Berteloot - Fabrizio Bianchi - Christophe Dupont -

Fuente: https://hal.archives-ouvertes.fr/



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