Arkiv för Matematik

  • Ark. Mat.
  • Volume 33, Number 2 (1995), 385-403.

Fractal dimensions for Jarník limit sets of geometrically finite Kleinian groups; the semi-classical approach

Bernd Stratmann

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Abstract

We introduce and study the Jarník limit set ℐσ of a geometrically finite Kleinian group with parabolic elements. The set ℐσ is the dynamical equivalent of the classical set of well approximable limit points. By generalizing the method of Jarník in the theory of Diophantine approximations, we estimate the dimension of ℐσ with respect to the Patterson measure. In the case in which the exponent of convergence of the group does not exceed the maximal rank of the parabolic fixed points, and hence in particular for all finitely generated Fuchsian groups, it is shown that this leads to a complete description of ℐσ in terms of Hausdorff dimension. For the remaining case, we derive some estimates for the Hausdorff dimension and the packing dimension of ℐσ.

Note

Research supported by the SFB 170 at the University of Göttingen

Article information

Source
Ark. Mat., Volume 33, Number 2 (1995), 385-403.

Dates
Received: 5 September 1994
Revised: 13 February 1995
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898478

Digital Object Identifier
doi:10.1007/BF02559716

Mathematical Reviews number (MathSciNet)
MR1373031

Zentralblatt MATH identifier
0851.30027

Rights
1995 © Institut Mittag-Leffler

Citation

Stratmann, Bernd. Fractal dimensions for Jarník limit sets of geometrically finite Kleinian groups; the semi-classical approach. Ark. Mat. 33 (1995), no. 2, 385--403. doi:10.1007/BF02559716. https://projecteuclid.org/euclid.afm/1485898478


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