Hausdorff dimension of the parameters for (α,β)-transformations with the specification property

2024/03/21 by Oguchi, Mai, Shinoda, Mao
#11K55 #37E05 #37E45 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.14230

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\citeSchmeling. 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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