Departmental Colloquium
Christian Wolf
CUNY Graduate Center
Computability of topological entropy and pressure for symbolic systems beyond finite type
Abstract: The computability of dynamically defined objects has been a subject of
intensive study over the past two decades. This includes important results
concerning the computability of invariant sets (e.g. Julia sets), entropies,
natural invariant measures, Lyapunov exponents, etc. In this talk we consider
symbolic dynamical systems given by the shift map on a finite alphabet-shift
space $X$. We identify the computability of the topological entropy
$h_{\rm top}(X)$ and topological pressure $P_{\rm top}(X,\phi)$ as a function
of the shift space $X$ and potential $\phi$. This question has previously
been studied by Burr et al., Hertling and Spandl, and Spandl in some
special cases. In this talk we address the computability question for
general shift spaces. One of our results states that the entropy function
$X\mapsto h_{\rm top}(X)$ is computable at a shift space $X_0$ iff $X_0$
has zero topological entropy.
Friday October 25, 2024 at 3:00 PM in 636 SEO