Complex Systems

Projectional Entropy in Higher Dimensional Shifts of Finite TypeDownload PDF

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 d where r < d. We show here that any projectional entropy is bounded below by the d 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.