SPECTRA OF RECURRENCE DIMENSION FOR DYNAMICALLY DEFINED SUBSETS OF RAUZY FRACTALS

Abstract

We compute the spectra of the recurrence dimension for dynamically defined subsets of Rauzy fractals, in the case when these sets are totally disconnected. These subsets of the Rauzy fractals are defined by subadic systems, therefore there is a well-defined dynamical system defined on them. The spectra of the recurrence dimension for adic and subadic systems was computed by the author in Sirvent,1and in the present article we extend those results to the dynamical systems mentioned before, which are geometrical realizations of these symbolic systems.This dimension is characterized by the Poincaré recurrence of the system, and the corresponding spectrum is invariant under bi-Lipschitz transformations.We also address the question, when the dynamically defined subsets of Rauzy Fractals are totally disconnected.