Displaying similar documents to “Constructions of smooth and analytic cocycles over irrational circle rotations”

Continued fractions and the Gauss map.

Bates, Bruce, Bunder, Martin, Tognetti, Keith (2005)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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The fractional dimensional theory in Lüroth expansion

Luming Shen, Kui Fang (2011)

Czechoslovak Mathematical Journal

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It is well known that every x ∈ ( 0 , 1 ] can be expanded to an infinite Lüroth series in the form of x = 1 d 1 ( x ) + ⋯ + 1 d 1 ( x ) ( d 1 ( x ) - 1 ) ⋯ d n - 1 ( x ) ( d n - 1 ( x ) - 1 ) d n ( x ) + ⋯ , where d n ( x ) ≥ 2 for all n ≥ 1 . In this paper, sets of points with some restrictions on the digits in Lüroth series expansions are considered. Mainly, the Hausdorff dimensions of the Cantor sets F φ = { x ∈ ( 0 , 1 ] : d n ( x ) ≥ φ ( n ) , ∀ n ≥ 1 } are completely determined, where φ is an integer-valued function defined on ℕ , and φ ( n ) → ∞ as n → ∞ .