Date of Award
Ronnie Pavlov, Ph.D.
Surface entropy, Entropy
Let χ be the class of 1-D and 2-D subshifts. This thesis defines a new function, HS : χ x R → [0,∞] which we call the surface entropy of a shift. This definition is inspired by the topological entropy of a subshift and we compare and contrast several structural properties of surface entropy to entropy. We demonstrate that much like entropy, the finiteness of surface entropy is a conjugacy invariant and is a tool in the classification of subshifts. We develop a tiling algorithm related to continued fractions which allows us to prove a continuity result about surface entropy in the 2-D case, namely that while it is only upper semicontinuous with respect to eccentricity that there are bounds on how badly discontinuous it can behave.
A known result about entropy is that the class of entropies of 2-D SFTs is the class of CFA numbers. In the second part of this thesis we show that all such CFA numbers can be realized as the surface entropy of a 2-D SFT. Furthermore we construct an example of a 2-D SFT demonstrating that the class of surface entropies is a strict superset to the class of entropies.
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Pace, Dennis, "Surface Entropy of Shifts of Finite Type" (2018). Electronic Theses and Dissertations. 1481.
Received from ProQuest