Substitutions, Partial Isometries of R, and Actions on Trees
نویسندگان
چکیده
In this paper we outline a connection between substitution dynamical systems and systems of partial isometries of R. Let τ be a primitive substitution and (X, T ) the associated minimal subshift. Associated to each real geometric realization G of τ is a system of partial isometries IG . The subshift (X, T ) generated by τ provides a symbolic coding of the dynamics of IG . This allows us to deduce various dynamical properties of the system: Minimality, classification (interval exchange, homogeneous, or exotic), orbit structure, independence of generators, and self similarity. We show by example that each type of minimal system of partial isometries can arise from geometric realizations of substitutions on three letters. These systems give rise to interesting (non-simplicial) geometric actions of free groups on real trees.
منابع مشابه
Substitutions, Partial Isometries of IR, and Actions on Trees
In this paper we outline a connection between substitution dynamical systems and systems of partial isometries of IR. Let τ be a primitive substitution and (X,T ) the associated minimal subshift. Associated to each real geometric realization G of τ is a system of partial isometries IG . The subshift (X,T ) generated by τ provides a symbolic coding of the dynamics of IG . This allows us to deduc...
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