Abstract.
This article shows how to approximate a stable action of a finitely presented group on an \( \Bbb {R} \)-tree by a simplicial one while keeping control over arc stabilizers. For instance, every small action of a hyperbolic group on an \( \Bbb {R} \)-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 \( \Bbb {R} \)-trees and on the dynamical study of exotic components by D. Gaboriau.
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Received: 22 October, 1997
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Guirardel, V. Approximations of stable actions on $ \Bbb {R} $-trees. Comment. Math. Helv. 73, 89–121 (1998). https://doi.org/10.1007/s000140050047
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DOI: https://doi.org/10.1007/s000140050047