Abstract
In this paper, we consider the specification property for ( α , β ) -shifts. When α = 0 , Schmeling shows that the set of β > 1 for which the β-shift has the specification property has the Lebesgue measure zero but has the full Hausdorff dimension [Schmeling. Symbolic dynamics for β-shifts and self-normal numbers, Ergodic Theory Dyn. Syst. 17 (1997), pp. 675–694]. So it is natural to ask what happens when α > 0 . Buzzi shows that for fixed α the set of β > 1 for which the ( α , β ) -shift has the specification property has Lebesgue measure zero. Hence we consider the Hausdorff dimension of the parameter space of ( α , β ) -shifts.
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