Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778937 | Indagationes Mathematicae | 2017 | 19 Pages |
Abstract
We investigate matching for the family Tα(x)=βx+α(mod1), αâ[0,1], for fixed β>1. Matching refers to the property that there is an nâN such that Tαn(0)=Tαn(1). We show that for various Pisot numbers β, matching occurs on an open dense set of αâ[0,1] and we compute the Hausdorff dimension of its complement. Numerical evidence shows more cases where matching is prevalent.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Henk Bruin, Carlo Carminati, Charlene Kalle,