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In this article, we study algebraic dynamical pairs $(f,a)$ parametrized byan irreducible quasi-projective curve $\Lambda$ having an absolutely continuousbifurcation measure. We prove that, if $f$ is non-isotrivial and $(f,a)$ isunstable, this is equivalent to the fact that $f$ is a family of Latt\`es maps.To do so, we prove the density of transversely prerepelling parameters in thebifucation locus of $(f,a)$ and a similarity property, at any transverselyprerepelling parameter $\lambda_0$, between the measure $\mu_{f,a}$ and themaximal entropy measure of $f_{\lambda_0}$. We also establish an equivalentresult for dynamical pairs of $\mathbb{P}^k$, under an additional assumption.

Dynamical pairs with an absolutely continuous bifurcation measure