Hausdorff dimension of sets of divergence arising from continued fractions

DOI10.1090/S0002-9939-2011-11032-3zbMath1267.37048OpenAlexW2035514823MaRDI QIDQ5389397

Ian Short

Publication date: 26 April 2012

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2011-11032-3

zbMATH Keywords

convergenceHausdorff dimensioncontinued fractionsdivergenceMöbius transformationsets of divergence

Mathematics Subject Classification ID

Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Continued fractions; complex-analytic aspects (30B70) Convergence and divergence of continued fractions (40A15) Möbius geometries (51B10)

Related Items (2)

The parabola theorem on continued fractions ⋮ Repeated compositions of Möbius transformations

Cites Work

• Convergence properties of sequences ol linear fractional transformations
• Sequences of linear fractional transformations
• Continued fractions. Vol. 1: Convergence theory
• Hausdorff dimension of certain sets arising in continued fraction expansions
• The limiting behavior of sequences of Moebius transformations
• Continued fractions, discrete groups and complex dynamics
• The Seidel, Stern, Stolz and Van Vleck Theorems on continued fractions
• General Convergence of Continued Fractions
• Conformal iterated function systems with applications to the geometry of continued fractions
• Conical limit sets and continued fractions
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