Dynamical pairs with an absolutely continuous bifurcation measure

Abstract

In this article, we study algebraic dynamical pairs (f, a) parametrized by an irreducible quasi-projective curve Λ having an absolutely continuous bifurcation measure. We prove that, if f is non-isotrivial and (f, a) is unstable, this is equivalent to the fact that f is a family of Lattès maps. To do so, we prove the density of transversely prerepelling parameters in the bifucation locus of (f, a) and a similarity property, at any transversely prerepelling parameter λ0, between the measure µ f,a and the maximal entropy measure of f λ 0 . We also establish an equivalent result for dynamical pairs of P k , under an additional assumption.