Lyapunov exponents and bifurcation current for polynomial-like maps

Abstract

We study holomorphic families of polynomial-like maps depending on a parameter s. We prove that the partial sums of largest Lyapunov exponents are plurisubharmonic functions of s. We also study their continuity and introduce the bifurcation locus as the support of bifurcation currents.

22 pages

Cited by in corpus (7)

• The Geometric Dynamical Northcott and Bogomolov Properties
• Dynamics of fibered endomorphisms of ${\mathbb{P}}^k$
• Attracting Currents and Equilibrium Measures for Quasi-attractors of ${\mathbb{P}}^k$
• Dynamics of horizontal-like maps in higher dimension
• Strong probabilistic stability in holomorphic families of endomorphisms of ${\mathbb{P}}^k(\mathbb{C})$ and polynomial-like maps
• Lyapunov exponents, bifurcation currents and laminations in bifurcation loci
• Continuity of Lyapunov exponents for polynomial automorphisms of ${\mathbb{C}}^2$