The Hausdorff dimension of bounded geodesics on geometrically finite manifolds

Ergodic Theory and Dynamical Systems

Volumn 17, Issue 1, 1997, Pages 227-246

  Stratmann, B ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031482818     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385797069800     Document Type: Article

References (23)

1. V. I. Arnold and A. Avez. Problèmes Ergodiques de la Mécanique Classique. Gauthier-Villars Éditeur, Paris, 1967.
2. A. F. Beardon. Inequalities for certain Fuchsian groups. Acta Math. 127 (1971), 221-258.
3. A. F. Beardon. The Geometry of Discrete Groups. Springer, New York, 1983.
4. C. J. Bishop and P. W. Jones. Hausdorff dimension and Kleinian groups. Preprint, Stony Brook, 1995.
5. B. H. Bowditch. Geometrical finiteness for hyperbolic groups. J. Func. Anal. 113 (1988), 245-317.
6. S. G. Dani. Bounded geodesics on manifolds of constant negative curvature. Preprint.
7. S. G. Dani. Bounded orbits of flows on homogeneous spaces. Comm. Math. Helvetici 61 (1986), 636-660.
8. K. Falconer. Fractal Geometry. Wiley, New York, 1990.
9. O. Frostman. Potential d'èquilibre et capacité des ensembles avec quelques applications à la théorie des fonctions. Meddel. Lunds Univ. Math. Sem. 3 (1935).
10. V. Jarnik. Zur metrischen Theorie der Diophantischen Approximationen. Prace Matematyczno-Fizyczne 36 2.Heft (1928), 91-106.
11. P. J. Nicholls. The Ergodic Theory of Discrete Groups (Lond. Math. Soc. Lecture Notes Series 143). Cambridge University Press, 1989.
12. S. J. Patterson. Diophantine approximation in Fuchsian groups. Phil. Trans. Roy. Soc. Lond. 282 (1976), 527-563.
13. S. J. Patterson. The limit set of a Fuchsian group. Acta Math. 136 (1976), 241-273.
14. S. J. Patterson. The exponent of convergence of Poincaré series. Monatshefte für Math. 82 (1976), 297-315.
15. S. J. Patterson. Lectures on measures on limit sets of Kleinian groups. Analytical and Geometric Aspects of Hyperbolic Space (Lond. Math. Soc. Lecture Notes Series 111). Cambridge University Press, 1987, pp. 281-323.
16. D. Ruelle. Thermodynamic Formalism (Encyclopedia of Mathematics and its Applications 5). Addison Wesley, 1976.
17. B. Stratmann. Diophantine approximation in Kleinian groups. Math. Proc. Cambr. Phil. Soc. 116 (1994), 57-78.
18. B. Stratmann. A note on counting cuspidal excursions. Annales Academiae Scientiarum Fennicae 20 (1995), 359-372.
19. B. Stratmann and M. Urbański. The box-counting dimension for geometrically finite Kleinian groups. Fundamenta Mathematicae 149 (1996), 83-93.
20. B. Stratmann and S. Velani. The Patterson measure for geometrically finite groups with parabolic elements, old and new. Proc. London Math. Soc. 71 (1995), 197-220.
21. D. Sullivan. The density at infinity of a discrete group. Inst. Hautes Etudes Sci. Publ. Math. 50 (1979), 171-202.
22. D. Sullivan. Entropy, Hausdorff measures old and new, and the limit set of geometrically finite Kleinian groups. Acta Math. 153 (1984), 259-277.
23. C. Tricot. Two definitions of fractional dimension. Math. Proc. Cambr. Phil. Soc. 91 (1982), 57-74.