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Diophantine approximation and Hausdorff dimension in Fuchsian groups

Published online by Cambridge University Press:  24 October 2008

S. L. Velani
S. L. Velani
Affiliation:
Department of Mathematics, University of York, Heslington, York Y01 5DD
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Extract

The Poincaré disc model

of two-dimensional hyperbolic space supports a metric ρ derived from the differential

Geodesics for the metric ρ are arcs of circles orthogonal to the unit circle S, and straight lines through the origin.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 2 , March 1993 , pp. 343 - 354
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

REFERENCES

[1]Baker, A. and Schmidt, W. M.. Diophantine approximation and Hausdorif dimension. Proc. London Math. Soc. (3) 21 (1970), 1–11.CrossRefGoogle Scholar
[2]Beardon, A. F.. The Geometry of Discrete Groups (Springer-Verlag, 1983).CrossRefGoogle Scholar
[3]Beardon, A. F.. The exponent of convergence of Poincaré series. Proc. London Math. Soc. (3) 18 (1968), 461–483.CrossRefGoogle Scholar
[4]Beardon, A F. and Nicholls, P. J.. On classical series associated with Kleinian groups. J. London Math. Soc. (2) 5 (1972), 645–655.CrossRefGoogle Scholar
[5]Besicovitch, A. S.. Sets of fractional dimension (IV): On rational approximation to real numbers. J. London Math. Soc. 9 (1934), 126–131.CrossRefGoogle Scholar
[6]Dodson, M. M., Rynne, B. P. and Vickers, J. A. G.. Diophantine approximation and a lower bound for Hausdorif dimension. Mathematika 37 (1990), 59–73.CrossRefGoogle Scholar
[7]Falconer, K. J.. Fractal Geometry – Mathematical Foundations and Applications (J. Wiley, 1990).CrossRefGoogle Scholar
[8]Jarnik, V.. Diophantische Approximationen und Hausdorffsches Mass. Mat. Sb. 36 (1929), 371–382.Google Scholar
[9]Melián, M. V. and Pestana, D.. Geodesic excursions into cusps in finite volume hyperbolic manifolds. Preprint.Google Scholar
[10]Patterson, S. J.. Lectures on measures on limit sets of Kleinian groups. In Analytic and Geometrical Aspects of Hyperbolic Space, London Math. Soc. Lecture Note Ser. no. 111 (Cambridge University Press, 1987), pp. 281–323.Google Scholar
[11]Patterson, S. J.. Diophantine approximation in Fuchsian groups. Philos. Trans. Roy. Soc. London Ser. A 282 (1976), 527–563.Google Scholar