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Diophantine approximation in Kleinian groups: singular, extremal, and bad limit points

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Publication details

JournalJournal of the London Mathematical Society
DateAccepted/In press - 2 Apr 2018
DateE-pub ahead of print - 20 Apr 2018
DatePublished (current) - 1 Oct 2018
Issue number2
Volume98
Number of pages23
Pages (from-to)306-328
Early online date20/04/18
Original languageEnglish

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.

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©2018 The Author(s)

    Research areas

  • 11J83, 11K60 (primary), 30F40 (secondary)

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