# Subsystems of transitive subshifts with linear complexity

## TL;DR

This paper establishes bounds on the number of minimal subsystems and generic measures in transitive subshifts with linear complexity, extending previous measure-theoretic results and providing new insights into their structural properties.

## Contribution

It introduces new bounds on minimal subsystems and generic measures in transitive subshifts with linear complexity, generalizing prior measure-theoretic results.

## Key findings

- Bound on the number of minimal subsystems based on complexity
- Bound on the number of generic measures supported
- Extension of measure-theoretic bounds to linear complexity subshifts

## 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].