Cd
C.J. de Jonge
5 records found
1
For N ∈ N≥2 and α ∈ R such that 0 < α ≤ N − 1, the continued fraction map Tα: [α, α+1] → [α, α+1) is defined as Tα (x):= N/x−d(x), where d: [α, α+1] → N is defined by d(x):= ⌊N/x − α⌋. A maximal open interval (a, b) ⊂ Iα is called a
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For N∈ N≥ 2 and α∈ R such that 0<α≤N-1, we define Iα: = [α, α+ 1] and Iα-:=[α,α+1) and investigate the continued fraction map Tα:Iα→Iα-, which is defined as Tα(x):=Nx-d(x), where d: Iα→ N is defined by d(x):=⌊Nx-α⌋. For N∈ N≥ 7, for
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In this thesis continued fractions are studied in three directions: semi-regular continued fractions, Nakada’s α-expansions and N-expansions. In Chapter 1 the general concept of a continued fraction is given, involving an operator that yields the partial quotients or digits of a
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Natural extensions for Nakada's α-expansions
Descending from 1 to g2
By means of singularisations and insertions in Nakada's α-expansions, which involves the removal of partial quotients 1 while introducing partial quotients with a minus sign, the natural extension of Nakada's continued fraction map Tα is given for (10-2)/3≤α<1. From our constr
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Three consecutive approximation coefficients
Asymptotic frequencies in semi-regular cases
Denote by p n /q n ,n=1,2,3,…, pn/qn,n=1,2,3,…,
the sequence of continued fraction convergents of a real irrational number x x
. Define the sequence of approximation coefficients by θ n (x):=q n |q n x−p n |,n=1,2,3,… θn(x):=qn|qnx−pn|,n=1,2,3,…
. In the case of regular conti
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