Metric theory for continued \(\beta \)-fractions

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Continued fractions and generalizations (11J70) Fractals (28A80) Metric theory of continued fractions (11K50)

Cites Work

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On sums of degrees of the partial quotients in continued fraction expansions of Laurent series
Continued fractions and numeration in the Fibonacci base
Hausdorff dimension of certain sets arising in continued fraction expansions
Asymptotic behavior of beta-integers
Continued fraction Cantor sets, Hausdorff dimension, and functional analysis
Representations of real numbers by infinite series
\(\beta\)-expansions and symbolic dynamics
Thermodynamic formalism and multifractal analysis of conformal infinite iterated function systems
Metric theorems for continued \(\beta\)-fractions
Diffraction spectra of weighted Delone sets on beta-lattices with beta a quadratic unitary Pisot number
Beta-expansion and continued fraction expansion
Representations for real numbers and their ergodic properties
On theβ-expansions of real numbers
The distribution of the largest digit in continued fraction expansions
Beta-integers as natural counting systems for quasicrystals
Conformal iterated function systems with applications to the geometry of continued fractions
On the fractional dimension of sets of continued fractions
Appendix to the paper by T. Łuczak—A simple proof of the lower
Dimensions and Measures in Infinite Iterated Function Systems
The shrinking target problem in the dynamical system of continued fractions
Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions ^*
Hausdorff dimension of some sets in the theory of continued beta-fractions and its generalized continued fractions

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