Computability of topological pressure on compact shift spaces beyond finite type​

Date. November 06, 14h00m (UTC/GMT)

Speaker. Christian Wolf (City University of New York)

Title. Computability of topological pressure on compact shift spaces beyond finite type​

Abstract.

In this talk we discuss the computability (in the sense of computable analysis) of the topological pressure $P_{\rm top}(\phi)$ on compact shift spaces $X$ for continuous potentials $\phi:X\to\bR$. This question has recently been studied for subshifts of finite type (SFTs) and their factors (Sofic shifts). We develop a framework to address the computability of the topological pressure on general shift spaces and apply this framework to coded shifts. In particular, we prove the computability of the topological pressure for all continuous potentials on S-gap shifts, generalized gap shifts, and Beta shifts. We also construct shift spaces which, depending on the potential, exhibit computability and non-computability of the topological pressure. We further show that the generalized pressure function $(X,\phi)\mapsto P_{\rm top}(X,\phi\vert_{X})$ is not computable for a large set of shift spaces $X$ and potentials $\phi$. Along the way of developing these computability results, we derive several ergodic-theoretical properties of coded shifts which are of independent interest beyond the realm of computability. The topic of the talk is joint work with Michael Burr (Clemson U.), Shuddho Das (NYU) and Yun Yang (Virginia Tech).

 

Online Zoom meeting (Session will open some minutes before 14h00)
https://videoconf-colibri.zoom.us/j/98242043162?pwd=Ym56N0xHUVJJV2dqWVFRbTkvVG9QQT09

Meeting ID: 982 4204 3162

Password: 785775

Date and Venue

Start Date
Venue
Online seminar

Speaker

Christian Wolf

Speaker's Institution

CUNY

Area

Dynamical Systems