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.
","abstract_html":"<p>Let χ be the class of 1-D and 2-D subshifts. This thesis defines a new function, H<sub>S</sub> : 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.</p> <p>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.</p>","abstract_has_math":false,"creators":["Pace, Dennis"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Ronnie Pavlov, Ph.D.","Nicholas Ormes","Alvaro Arias","Brian Majestic"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-08-01T07:00:00Z","date_published":"2018-08-01T07:00:00Z","updated_at":"2026-07-24T02:03:19Z","subjects":["Surface entropy","Entropy","Mathematics","Physical Sciences and Mathematics"],"languages":["en"],"rights":["Copyright is held by the author. User is responsible for all copyright compliance.
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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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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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"],"dc:subject":["Surface entropy","Entropy","Mathematics","Physical Sciences and Mathematics"],"dc:title":["Surface Entropy of Shifts of Finite Type"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T02:03:19Z"}