We consider shift maps on finite alphabet shift spaces and discuss questions concerning the computability (in the sense of computable analysis) of relevant thermodynamic invariants such as entropy, topological pressure and residual entropy. These questions have been recently studied for subshifts of finite type (SFTs) and their factors (sofic shifts) by Spandl, Hertling and Spandl, and Burr, Schmoll and Wolf. In this talk we consider possible extensions to more general classes of shift spaces including S-gap shifts, beta-shifts and bounded density shifts. Several positive computability results will be presented but we also show that for certain shifts even the entropy is not computable.
The results presented in this talk are part of an on-going collaboration with M. Burr (Clemson), S. Das (NYU) and Y. Yang (Virginia Tech).