Pseudogroups of isometries of R: reconstruction of free actions on R-trees

D. Gaboriau, G. Levitt and F. Paulin

Article publié :

Erg. Th. Dyn. Syst 15 (1994) 1-20.

lien vers Ergodic Theory and Dynamical Systems

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The theorem of Rips about free actions on R-trees relies on a careful analysis of finite systems of partial isometries of R. In this paper we associate a free action on an R-tree to any finite system of isometries without reflection. Any free action may be approximated (strongly in the sense of Gillet-Shalen) by actions arising in this way. Proofs use in an essential way separation properties of systems of isometries. We also interpret these finite systems of isometries as generating sets of pseudogroups of partial isometries between closed intervals of R.