## Abstract

For any real T, a lim sup set WGty (T) of T-(well)-approximabl e

points is defined for discrete groups ~ acting on the Poincar é

model of hyperbolic space . Here y is a ` distinguished point ' on

the sphere at infinity whose orbit under G corresponds to the rationals

(which can be regarded as the orbit of the point at infinity

under the modular group) in the classical theory of diophantin e

approximation .

In this paper the Hausdorff dimension of the set WG, y (T} is determined

for geometrically finite groups of the first kind . Consequently,

by considering the hyperboloid model of hyperbolic space ,

this result is shown to have a natural but non trivial interpretatio n

in terms of quadratic forms .

points is defined for discrete groups ~ acting on the Poincar é

model of hyperbolic space . Here y is a ` distinguished point ' on

the sphere at infinity whose orbit under G corresponds to the rationals

(which can be regarded as the orbit of the point at infinity

under the modular group) in the classical theory of diophantin e

approximation .

In this paper the Hausdorff dimension of the set WG, y (T} is determined

for geometrically finite groups of the first kind . Consequently,

by considering the hyperboloid model of hyperbolic space ,

this result is shown to have a natural but non trivial interpretatio n

in terms of quadratic forms .

Original language | English |
---|---|

Pages (from-to) | 175-185 |

Number of pages | 11 |

Journal | Publicacions Matematique |

Volume | 38 |

Issue number | 1 |

Publication status | Published - 1994 |