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].

30 pages, 0 figures

References in corpus (1)

• On the number of ergodic measures for minimal shifts with eventually constant complexity growth

Cited by in corpus (2)

• Word Complexity of (Measure-Theoretically) Weakly Mixing Rank-One Subshifts
• Slow entropy and variational dynamical systems