We investigate matching for the family Tα(x)=βx+α(mod1), α∈[0,1], for fixed β>1. Matching refers to the property that there is an n∈N such that Tα^n(0)=Tα^n(1). We show that for various Pisot numbers β, matching occurs on an open dense set of α∈[0,1] and we compute the Hausdorff dimension of its complement. Numerical evidence shows more cases where matching is prevalent.
Matching for generalised beta-transformations
CARMINATI, CARLO;
2017-01-01
Abstract
We investigate matching for the family Tα(x)=βx+α(mod1), α∈[0,1], for fixed β>1. Matching refers to the property that there is an n∈N such that Tα^n(0)=Tα^n(1). We show that for various Pisot numbers β, matching occurs on an open dense set of α∈[0,1] and we compute the Hausdorff dimension of its complement. Numerical evidence shows more cases where matching is prevalent.File in questo prodotto:
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