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 |