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Computability Theoretic Properties of the Entropy of Gap Shifts

First, we analyse the computability theoretic relationship between the defining set S of a "gap shift" and the language of the gap shift. Therefore, we look at various computability theoretic conditions that the set S of a gap shift or the language of a gap shift might satisfy: decidability, computable enumerability, and computable enumerability of the complement. Then we look at the topological entropy of a gap shift and analyse the relationship between on the one hand the various kinds of computability theoretic conditions on a gap shift that we just mentioned and on the other hand various kinds of computability theoretic conditions on the entropy resp. on any real number in the unit interval: computability, left-computability, and right-computability.