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

François Berteloot (1) , Christophe Dupont (2)

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

We introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of CP(k). We characterize the corresponding bifurcations by the strict subharmonicity of the sum of Lyapunov exponents, by the instability of repelling cycles or the instability of critical dynamics. Our methods are based on ergodic theory and on pluripotential theory.

Mots clés: holomorphic dynamics; dynamical stability; positive currents; Lyapunov exponents

Domaines: Systèmes dynamiques [math.DS]; Variables complexes [math.CV]

François Berteloot, Christophe Dupont. Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k). 2014. ⟨hal-00967542v1⟩