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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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