#### Title

Projectional Entropy In Higher Dimensional Shifts Of Finite Type

#### 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.

#### 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.

http://works.swarthmore.edu/fac-math-stat/141