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A generalization of the Jarník–Besicovitch theorem by continued fractions
Ergodic Theory and Dynamical Systems, 2015We apply the tools of continued fractions to tackle the Diophantine approximation, including the classic Jarník–Besicovitch theorem, localized Jarník–Besicovitch theorem and its several generalizations. As is well known, the classic Jarník–Besicovitch sets, expressed in terms of continued fractions, can be written as $$\begin{eqnarray}\{x\in [0,1):a_{n+
Wang, Bao-Wei, Wu, Jun, Xu, Jian
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Generalized continued fractions associated with the Gauss transform
Russian Mathematical Surveys, 2002In this short note the author describes some properties of the so-called \(\omega\)-continued fractions \(x=[a_0,a_1,\dots]_\omega\), which are a one-dimensional variant of the multidimensional \((A,\omega)\)-continued fractions, which was introduced by the author in [Math. Notes 56, No. 6, 1315--1317 (1994); translation from Mat. Zametki 56, No.
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Other Generalizations of Continued Fractions
Algorithms and Computation in Mathematics, 2022Oleg N Karpenkov, Karpenkov Oleg N
exaly
Combinatorial properties of multidimensional continued fractions
Discrete Mathematics, 2023Michele Battagliola, Nadir Murru
exaly
Generalized Notions of Continued Fractions
2023Juan Fernández Sánchez +3 more
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Dependence with complete connections and the Gauss–Kuzmin theorem for N-continued fractions
Journal of Mathematical Analysis and Applications, 2016Dan Lascu
exaly
A further generalization of the continued fraction
Doklady Mathematics, 2006A. D. Bruno, V. I. Parusnikov
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