Skip to Main Content

Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Conical limit sets and continued fractions
HTML articles powered by AMS MathViewer

by Edward Crane and Ian Short PDF
Conform. Geom. Dyn. 11 (2007), 224-249 Request permission

Abstract:

Inspired by questions of convergence in continued fraction theory, Erdős, Piranian and Thron studied the possible sets of divergence for arbitrary sequences of Möbius maps acting on the Riemann sphere, $S^2$. By identifying $S^2$ with the boundary of three-dimensional hyperbolic space, $H^3$, we show that these sets of divergence are precisely the sets that arise as conical limit sets of subsets of $H^3$. Using hyperbolic geometry, we give simple geometric proofs of the theorems of Erdős, Piranian and Thron that generalise to arbitrary dimensions. New results are also obtained about the class of conical limit sets; for example, it is closed under locally quasisymmetric homeomorphisms. Applications are given to continued fractions.
References
Similar Articles
  • Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2000): 51B10, 40A15
  • Retrieve articles in all journals with MSC (2000): 51B10, 40A15
Additional Information
  • Edward Crane
  • Affiliation: Department of Mathematics, University Walk, Bristol, BS8 1TW, United Kingdom
  • Email: Edward.Crane@gmail.com
  • Ian Short
  • Affiliation: Logic House, National University of Ireland, Maynooth, Maynooth, County Kildare, Ireland
  • MR Author ID: 791601
  • ORCID: 0000-0002-7360-4089
  • Email: Ian.Short@nuim.ie
  • Received by editor(s): January 3, 2007
  • Published electronically: October 31, 2007
  • Additional Notes: The first author was supported by a junior research fellowship at Merton College, Oxford, and by the University of Bristol.
    The second author was supported by Science Foundation Ireland grant 05/RFP/MAT0003.
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 11 (2007), 224-249
  • MSC (2000): Primary 51B10; Secondary 40A15
  • DOI: https://doi.org/10.1090/S1088-4173-07-00169-5
  • MathSciNet review: 2354097