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be a continuous dynamical system on a compact metric space
-dimensional continuous potential. The (generalized) rotation set
is defined as the set of all
runs over all invariant probability measures. Analogous to the classical topological entropy, one can associate the localized entropy
. In this paper, we study the computability of rotation sets and localized entropy functions by deriving conditions that imply their computability. Then we apply our results to study the case where
is a subshift of finite type. We prove that
is computable and that
is computable in the interior of the rotation set. Finally, we construct an explicit example that shows that, in general,
is not continuous on the boundary of the rotation set when considered as a function of
. In particular,
is, in general, not computable at the boundary of
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