Dual Systems of algebraic iterated function systems, Rauzy fractals and β-tilings
نویسندگان
چکیده
Algebraic GIFS is a class of graph-directed iterated function systems (IFS) on R with algebraic parameters. A dual IFS of an algebraic GIFS can be constructed, and the duality between the two systems and has been investigated from various points of view. We review the results of dual IFS concerning the open set condition, purely periodic codings and the Rauzy-Thurston tilings, and their relation with previous studies. Either a substitution or a numeration system can define an algebraic IFS in a natural way, and both Rauzy fractals and β-tilings can be obtained as dual IFS. The dual IFS provides a unified and simple framework for the theory of Rauzy fractals, β-tilings and related studies. §
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