Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces / Lior Fishman, David Simmons, Mariusz Urbański.

"In this paper, we provide a complete theory of Diophantine approximation in the limit set of a group acting on a Gromov hyperbolic metric space. This summarizes and completes a long line of results by many authors, from Patterson's classic '76 paper to more recent results of Hersonsk...

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Bibliographic Details
Online Access: Online Access
Main Authors: Fishman, Lior, 1964- (Author), Simmons, David, 1988- (Author), Urbański, Mariusz (Author)
Format: Manuscript eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, 2018.
Series:Memoirs of the American Mathematical Society ; no. 1215.
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Table of Contents:
  • Introduction
  • Gromov hyperbolic metric spaces
  • Basic facts about Diophantine approximation
  • Schmidt's game and McMullen's absolute game
  • Partition structures
  • Proof of Theorem 6.1 (Absolute winning...)
  • Proof of Theorem 7.1 (Generalization of the Jarník-Besicovitch Theorem)
  • Proof of Theorem 8.1 (Generalization of Khinchin's Theorem)
  • Proof of Theorem 9.3 (BA [subscript]d has full dimension in [lambda][subscript]r (G))
  • Appendix A. Any function is an orbital counting function for some parabolic group
  • Appendix B. Real, complex, and quaternionic hyperbolic spaces
  • Appendix C. The potential function game
  • Appendix D. Proof of Theorem 6.1 using the H-potential game, where H = points
  • Appendix E. Winning sets and partition structures.