Speedups of linearly recurrent subshifts

Abstract

A speedup, like a time change in discrete time dynamics, is a way of moving faster through the orbits of a dynamical system. Linearly recurrence is a stronger form of minimality for subshifts, shared by e.g.\ all primitive substitution shifts and Sturmian shifts associated with rotation numbers of bounded type. We prove that the homeomorphic speedup of a linearly recurrent two-sided subshift is again linearly recurrent.

Lemma 3.2 corrected from the earlier version, and changes made accordingly. Section 4 rewritten, proof of Lemma 4.1 corrected