Weak singularity spectra of the patterson measure for geometrically finite Kleinian groups with parabolic elements

Michigan Mathematical Journal

Volumn 46, Issue 3, 1999, Pages 573-587

  Stratmann, Bernd O ^a  

^a UNIVERSITY OF ST ANDREWS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011055458     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1030132480     Document Type: Article

References (20)

1. A. F. Beardon, Inequalities for certain Fuchsian groups, Acta Math. 127 (1971), 221-258.
2. A. S. Besicovitch, Sets of fractional dimenions (IV): On rational approximation to real numbers, J. London. Math. Soc. (2) 9 (1934), 126-131.
3. C. J. Bishop and P. W. Jones, Hausdorff dimension and Kleinian groups, Acta Math. 179 (1997), 1-39.
4. K. Falconer, Fractal geometry: Mathematical foundations and applications, Wiley, New York, 1990.
5. R. Hill and S. L. Velani, The Jarník-Besicovitch theorem for geometrically finite Kleinian groups, Proc. London Math. Soc. (3) 77 (1998), 524-550.
6. V. Jarník, Diophantische Approximationen und Hausdorff Mass, Mat. Sb. 36 (1929), 371-382.
7. M. Melián and D. Pestana, Geodesic excursions into cusps in finite-volume hyperbolic manifolds, Michigan Math. J. 40 (1993), 77-93.
8. P. J. Nicholls, The ergodic theory of discrete groups, London Math. Soc. Lec. Notes Ser., 143, Cambridge Univ. Press, Cambridge, 1989.
9. S. J. Patterson, The limit set of a Fuchsian group, Acta Math. 136 (1976), 241-273.
10. -, Lectures on measures on limit sets of Kleinian groups, London. Math. Soc. Lec. Notes Ser., 111, pp. 28-323, Cambridge Univ. Press, Cambridge, 1987.
11. M. Policott and H. Weiss, Multifractal analysis for the continued fraction and Manneville-Pomeau transformation and applications to Diophantine approximation, preprint, 1998.
12. B. Stratmann, Fractal dimensions for Jarník limit sets; the semi-classical approach, Ark. Mat. 33 (1995), 385-403.
13. -, The Hausdorff dimension of bounded geodesics on geometrically finite manifolds, Ergodic Theory Dynamical Systems 17 (1997), 227-246.
14. -, Multiple fractal aspects of conformal measures; a survey, Workshop on fractals and dynamics (M. Denker, S.-M. Heinemann, B. Stratmann, eds.), Math. Gottingensis, 5, pp. 65-71, Springer-Verlag, Berlin, 1997.
15. B. Stratmann and M. Urbański, Jarník and Julia; a Diophantine analysis for parabolic rational maps, preprint, 1999.
16. -, The geometry of conformal measures of parabolic rational maps, Math. Proc. Cambridge Philos. Soc. 127 (1999).
17. B. Stratmann and S. L. Velani, The Patterson measure for geometrically finite groups with parabolic elements, new and old, Proc. London. Math. Soc. (3) 71 (1995), 197-200.
18. D. Sullivan, The density at infinity of a discrete group of hyperbolic motions, Études Sci. Publ. Math. 50 (1979), 171-202.
19. -, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta. Math. 153 (1984), 259-277.
20. -, Conformal dynamical systems, Lecture Notes in Math., 1007, Springer-Verlag, Berlin.