Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The linear escape limit set


Author: Christopher J. Bishop
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1385-1388
MSC (2000): Primary 30F35
Published electronically: December 5, 2003
MathSciNet review: 2053343
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $G$ 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 [Enhancements On Off] (What's this?)

  • 1. Christopher J. Bishop and Peter W. Jones, Hausdorff dimension and Kleinian groups, Acta Math. 179 (1997), no. 1, 1–39. MR 1484767, 10.1007/BF02392718
  • 2. T. Lundh.
    Geodesics on quotient manifolds and their corresponding limit points.
    Michigan Math. J. 51:279-304, 2003.
  • 3. Pertti Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge Studies in Advanced Mathematics, vol. 44, Cambridge University Press, Cambridge, 1995. Fractals and rectifiability. MR 1333890
  • 4. Curtis T. McMullen, Renormalization and 3-manifolds which fiber over the circle, Annals of Mathematics Studies, vol. 142, Princeton University Press, Princeton, NJ, 1996. MR 1401347
  • 5. Peter J. Nicholls, The ergodic theory of discrete groups, London Mathematical Society Lecture Note Series, vol. 143, Cambridge University Press, Cambridge, 1989. MR 1041575

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: http://dx.doi.org/10.1090/S0002-9939-03-07095-3
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
Published electronically: December 5, 2003
Additional Notes: The author was partially supported by NSF Grant DMS 0103626
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2003 American Mathematical Society