Projectional Entropy In Higher Dimensional Shifts Of Finite Type

Authors

Aimee S. A. Johnson, Swarthmore CollegeFollow
S. Kass
K. M. Madden

Document Type

Article

Publication Date

2007

Published In

Complex Systems

Abstract

Any higher dimensional shift space (X, ℤᵈ) contains many lower dimensional shift spaces obtained by projection onto r-dimensional sublattices L of ℤᵈ where r < d. We show here that any projectional entropy is bounded below by the ℤᵈ entropy and, in the case of certain shifts of finite type satisfying a mixing condition, equality is achieved if and only if the shift of finite type is the infinite product of a lower dimensional projection.

Comments

This work is freely available courtesy of Complex Systems.

Recommended Citation

Aimee S. A. Johnson, S. Kass, and K. M. Madden. (2007). "Projectional Entropy In Higher Dimensional Shifts Of Finite Type". Complex Systems. Volume 17, Issue 3. 243-257.
https://works.swarthmore.edu/fac-math-stat/141