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Construction of the compact core of a real tree by tree substitution. (Construction du cœur compact d’un arbre réel par substitution d’arbre.) (French. English summary) Zbl 1277.37022
Summary: Let $$\sigma$$ be an automorphism of the free group. Using a train-track representative of its inverse, one can construct the repelling tree $$T$$ of $$\sigma$$. The free group acts on $$T$$ by isometries. The dynamical system generated by $$\sigma$$ can be interpreted geometrically by the action of the free group restricted to a compact subset of the metric completion of $$T$$. This article gives a construction of this subset on a class of examples by introducing tree substitutions. We will insist on the connections between the construction using a tree substitution and the initial symbolic dynamical system.

##### MSC:
 37B10 Symbolic dynamics 20E08 Groups acting on trees 20F65 Geometric group theory
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##### References:
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