Surface Entropy of Shifts of Finite Type

<p>Let χ be the class of 1-D and 2-D subshifts. This thesis defines a new function, H_S : 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>

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Year dc:date.available

2018

Author dc:creator

• Pace, Dennis

Contributors dc:contributor

• Ronnie Pavlov, Ph.D.
• Nicholas Ormes
• Alvaro Arias
• Brian Majestic

• Surface entropy
• Entropy
• Mathematics
• Physical Sciences and Mathematics

Statement dc:rights

• <p>Copyright is held by the author. User is responsible for all copyright compliance.</p>

Language dc:language

en

Repository record dc:identifier

https://digitalcommons.du.edu/etd/1481

OAI identifier oai:identifier

oai:digitalcommons.du.edu:etd-2481