Projectional Entropy in Higher Dimensional Shifts of Finite Type
Aimee Johnson
Electronic mail address: aimee@swarthmore.edu
Department of Mathematics and Statistics,
Swarthmore College, Swarthmore, PA 19081
Steve Kass
Electronic mail address: skass@drew.edu
Department of Mathematics and Computer Science,
Drew University, Madison, NJ 07940
Kathleen Madden
Electronic mail address: kmadden@drew.edu
Department of Mathematics and Computer Science,
Drew University, Madison, NJ 07940
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.
https://doi.org/10.25088/ComplexSystems.17.3.243
