Conical limit sets and continued fractions

DOI10.1090/S1088-4173-07-00169-5zbMath1172.30001arXiv0708.1730OpenAlexW1968735989MaRDI QIDQ5448895

Ian Short, Edward Crane

Publication date: 7 March 2008

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.1730

zbMATH Keywords

Diophantine approximationhyperbolic geometrycontinued fractionquasiconformal mappingconical limit set

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Continued fractions; complex-analytic aspects (30B70) Convergence and divergence of continued fractions (40A15) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35) Möbius geometries (51B10)

Related Items (2)

Hausdorff dimension of sets of divergence arising from continued fractions ⋮ The parabola theorem on continued fractions

Cites Work

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• Convergence properties of sequences ol linear fractional transformations
• Sequences of linear fractional transformations
• Quasiconformal extension from dimension n to n+1
• Lectures on hyperbolic geometry
• Conformal geometry and quasiregular mappings
• The limiting behavior of sequences of Moebius transformations
• The pointwise convergence of Möbius maps
• Continued fractions, discrete groups and complex dynamics
• Continued fractions and restrained sequences of Möbius maps
• General Convergence of Continued Fractions

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