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Diophantine approximation in Kleinian groups: singular, extremal, and bad limit points
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Diophantine approximation in Kleinian groups
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Diophantine approximation in Kleinian groups - singular, extremal, and bad limit points
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Publication details
| Journal | Journal of the London Mathematical Society |
|---|---|
| Date | Accepted/In press - 2 Apr 2018 |
| Date | E-pub ahead of print - 20 Apr 2018 |
| Date | Published (current) - 1 Oct 2018 |
| Issue number | 2 |
| Volume | 98 |
| Number of pages | 23 |
| Pages (from-to) | 306-328 |
| Early online date | 20/04/18 |
| Original language | English |
Abstract
The overall aim of this note is to initiate a ‘manifold’ theory for metric Diophantine approximation on the limit sets of Kleinian groups. We investigate the notions of singular and extremal limit points within the geometrically finite Kleinian group framework. Also, we consider the natural analogue of Davenport's problem regarding badly approximable limit points in a given subset of the limit set. Beyond extremality, we discuss potential Khintchine-type statements for subsets of the limit set. These can be interpreted as the conjectural ‘manifold’ strengthening of Sullivan's logarithmic law for geodesics.
Bibliographical note
©2018 The Author(s)
- 11J83, 11K60 (primary), 30F40 (secondary)
Research areas
Projects
Programme Grant-New Frameworks in metric Number Theory
Project: Research project (funded) › Research
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