Approximations of stable actions on R-trees

This article shows how to approximate a stable action of a finitely presented group on an B-tree by a simplicial one while keeping control over are stabilizers. For instance, every small action of a hyperbolic group on an R-tree can be approximated by a small action of the same group on a simplicial tree. The techniques we use highly rely on Rips's study of stable actions on R-trees and on the dynamical study of exotic components by D. Gaboriau.