Self-similar sets. III: Constructions with sofic systems. (English) Zbl 0712.58039

Bandt, Christoph

Monatsh. Math. 108, No. 2-3, 89-102 (1989).

Summary: [For part I see the author, Math. Nachr. 142, 107-123 (1989; Zbl 0707.28004), for part IV see Proc. Conf. Topology and Measure V, Greifswald, 8-16 (1988).]
Using sofic systems, modifications of the self-similar sets of Hutchinson are defined as solutions of systems of fixed-point equations. Their Hausdorff dimension is determined.

MSC:

37A99	Ergodic theory
28D05	Measure-preserving transformations
37E99	Low-dimensional dynamical systems

Keywords:

symbolic dynamics; similarity-invariant measure; sofic systems; fixed- point equations; Hausdorff dimension

Citations:

Zbl 0707.28004

References:

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