Subsystems of transitive subshifts with linear complexity

Abstract: We bound the number of distinct minimal subsystems of a given transitive subshift of linear complexity, continuing work of Ormes and Pavlov [7]. We also bound the number of generic measures such a subshift can support based on its complexity function. Our measure-theoretic bounds generalize those of Boshernitzan [1] and are closely related to those of Cyr and Kra [2].