Bowen’s formula for shift-generated finite conformal constructions. (English) Zbl 1390.28008

The authors study shift-generated finite conformal constructions, i.e., conformal constructions generated by a general shift over a finite alphabet. Their constructions are not restricted to shifts of finite type or sofic shifts as in the classical limit set constructions. In particular, they prove that the limit sets of such constructions satisfy Bowen’s formula, which gives the Hausdorff dimension of the limit set as the zero of the topological pressure. Several examples are presented, including an one-dimensional construction generated by the so-called context-free shift.


28A78 Hausdorff and packing measures
28A80 Fractals
37B10 Symbolic dynamics
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