Seeing structure and complexity in subshifts
May 16 2013 – 3:00pm – 4:00 pm
Karl Petersen (University of North Carolina at Chapel Hill)
In joint work with Kathleen Carroll and Benjamin Wilson, we explore two ways to study properties of topological dynamical systems, especially subshifts. The first is by constructing Markov diagrams, following the ideas of Weiss, Fischer, Krieger, Hofbauer, and Buzzi. It turns out that interesting such diagrams can be displayed even for highly structured, infinite memory, fundamentally non-Markovian systems, such as Sturmian and substitution subshifts. The second is a variation on entropy. Edelman, Sporns, and Tononi proposed a concept called “intricacy” to measure complexity or interconnectivity of neural networks, and Buzzi and Zambotti studied it for families of random variables. We define a version for topological dynamical systems and examine some of its properties, including comparison with topological entropy.