Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

The linear escape limit set

Author(s): Christopher J. Bishop
Journal: Proc. Amer. Math. Soc. 132 (2004), 1385-1388.
MSC (2000): Primary 30F35
Posted: December 5, 2003
MathSciNet review: 2053343
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: If is any Kleinian group, we show that the dimension of the limit set $\Lambda$ is always equal to either the dimension of the bounded geodesics or the dimension of the geodesics that escape to infinity at linear speed.

References:

1.: C. J. Bishop and P. W. Jones.
Hausdorff dimension and Kleinian groups.
Acta. Math. 179:1-39, 1997. MR 98k:22043
2.: T. Lundh.
Geodesics on quotient manifolds and their corresponding limit points.
Michigan Math. J. 51:279-304, 2003.
3.: P. Mattila.
Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability.
Cambridge Studies in Advanced Mathematics 44. Cambridge University Press, Cambridge, 1995. MR 96h:28006
4.: C. T. McMullen.
Renormalization and -manifolds which fiber over the circle.
Annals of Mathematics Studies 142. Princeton University Press, Princeton, NJ, 1996. MR 97f:57022
5.: P. J. Nicholls.
The ergodic theory of discrete groups.
London Mathematical Society Lecture Note Series 143. Cambridge University Press, 1989. MR 91i:58104

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30F35

Retrieve articles in all Journals with MSC (2000): 30F35

Additional Information:

Christopher J. Bishop
Affiliation: Mathematics Department, SUNY at Stony Brook, Stony Brook, New York 11794-3651
Email: bishop@math.sunysb.edu

DOI: 10.1090/S0002-9939-03-07095-3
PII: S 0002-9939(03)07095-3
Keywords: Hausdorff dimension, quasi-Fuchsian groups, quasiconformal deformation, critical exponent, convex core
Received by editor(s): May 22, 2002
Received by editor(s) in revised form: October 30, 2002
Posted: December 5, 2003
Additional Notes: The author was partially supported by NSF Grant DMS 0103626
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2003, American Mathematical Society

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|