Limit Points Badly Approximable by Horoballs

Details Limit Points Badly Approximable by Horoballs Limit Points Badly Approximable by Horoballs

2012-01-21

arxiv.org/abs/1201.4505v2

Mathematics

Metric Geometry

13 pages

Scientific paper

For a proper, geodesic, Gromov hyperbolic metric space X, a discrete subgroup of isometries \Gamma whose limit set is uniformly perfect, and a disjoint collection of horoballs {H_j}, we show that the set of limit points badly approximable by {H_j} is absolutely winning in the limit set. As an application, we deduce that for a geometrically finite Kleinian group acting on H^{n+1}, the limit points badly approximable by parabolics is absolutely winning, generalizing previous results of Dani and McMullen. As a consequence of winning, we show that the set of badly approximable limit points has dimension equal to the critical exponent of the group. Since this set can alternatively be described as the limit points representing bounded geodesics in the quotient H^{n+1}/\Gamma, we recapture a result originally due to Bishop and Jones.

Affiliated with

Also associated with

No associations

Rating

Limit Points Badly Approximable by Horoballs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Limit Points Badly Approximable by Horoballs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Limit Points Badly Approximable by Horoballs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-482617