arXiv subjects
Publications and source records attributed to Arnaud Nerrière.
We consider iterated preimages of curves by random products of birational transformations of the plane. Following a recent work of Diller and Roeder, we study the action of the Cremona group on the inverse limit of the spaces of currents in all models of the plane. We show equidistribution for generic finitely supported random walks.
Let $μ$ be a finitely supported probability measure on the group of automorphisms of $\mathbb{A}^2_\mathbb{C}$. If the group generated by the support of $μ$ is non-elementary and contains only loxodromic elements, we show the existence of dynamical Green functions associated to random products. We derive consequences for $μ$-stationary measures: they are compactly supported, and we can apply Roda's theorem to show stiffness when the action is non-dissipative.