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Nowak, W. Georg; Scheicher, Klaus; Sirvent, Víctor F.

On Hausdorff dimension monotonicity of a family of dynamical subsets of Rauzy fractals. (English) Zbl 1418.37023

Int. J. Number Theory 11, No. 4, 1089-1098 (2015).
Summary: We consider a family of dynamically defined subsets of Rauzy fractals in the plane. These sets were introduced in the context of the study of symmetries of Rauzy fractals. We prove that their Hausdorff dimensions form an ultimately increasing sequence of numbers converging to 2. These results answer a question stated by the third author in [Unif. Distrib. Theory 7, No. 1, 155–171 (2012; Zbl 1313.11048)].

Cited in 1 Document

MSC:

37B10 Symbolic dynamics
28A80 Fractals
11B85 Automata sequences
11N37 Asymptotic results on arithmetic functions

Keywords:

Rauzy fractals; Hausdorff dimension; finite automata; asymptotic expansions

Citations:

Zbl 1313.11048
Cite Review PDF
Full Text: DOI

References:

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