Mathematics Research Seminar Series: Periodic Points in Rectangular-Preserving Random Substitution Subshifts

Mathematics Research Seminar Series
Periodic Points in Rectangular-Preserving Random Substitution Subshifts

by Bryan Ceasar L. Felipe

Date: Wednesday, 16 November 2022
Time: 4:00 pm
Venue: https://bit.ly/AdmuMathSeminar

Abstract. We investigate the existence of periodic points in subshifts associated to rectangular-preserving random substitutions. We give a necessary criterion for primi- tive compatible rectangular-preserving random substitutions to admit periodic points in their subshifts. A stronger criterion is provided for the case of block random substi- tutions. Moreover, we present an algorithm that determines if a rectangular word is a valid periodic block for a periodic point in a rectangular-preserving random substitution subshift.

Keywords: random substitution, rectangular-preserving substitution, periodic points, symbolic dynamics