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ℝ-trees, dual laminations and compact systems of partial isometries

Published online by Cambridge University Press:  01 September 2009

THIERRY COULBOIS ,
ARNAUD HILION  and
MARTIN LUSTIG
THIERRY COULBOIS
Affiliation:
LATP, Université Aix-Marseille III, Marseille, France. e-mail: thierry.coulbois@univ-cezanne.fr, arnaud.hilion@univ-cezanne.fr, martin.lustig@univ-cezanne.fr
ARNAUD HILION
Affiliation:
LATP, Université Aix-Marseille III, Marseille, France. e-mail: thierry.coulbois@univ-cezanne.fr, arnaud.hilion@univ-cezanne.fr, martin.lustig@univ-cezanne.fr
MARTIN LUSTIG
Affiliation:
LATP, Université Aix-Marseille III, Marseille, France. e-mail: thierry.coulbois@univ-cezanne.fr, arnaud.hilion@univ-cezanne.fr, martin.lustig@univ-cezanne.fr
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Abstract

Let FN be a free group of finite rank N ≥ 2, and let T be an ℝ-tree with a very small, minimal action of FN with dense orbits. For any basis of FN there exists a heart ⊂ (= the metric completion of T) which is a compact subtree that has the property that the dynamical system of partial isometries ai : , for each ai ∈ , defines a tree which contains an isometric copy of T as minimal subtree.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 2 , September 2009 , pp. 345 - 368
Copyright
Copyright © Cambridge Philosophical Society 2009

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