Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computability of topological pressure on compact shift spaces beyond
  finite type   We investigate the computability (in the sense of computable analysis) of the
topological pressure $P_{\rm top}(\phi)$ on compact shift spaces $X$ for
continuous potentials $\phi:X\to {\mathbb R}$. 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 particular
Beta-shifts. We also construct shift spaces which, depending on the potential,
exhibit computability and non-computability of the topological pressure. We
further prove 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 $\phi$. In particular, the entropy map $X\mapsto h_{\rm top}(X)$
is computable at a shift space $X$ if and only if $X$ has zero topological
entropy. 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.

18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
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The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
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The categories of this paper are: eess
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs