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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| Online Access: |
Online Access |
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| Main Authors: | , , |
| Format: | Manuscript eBook |
| Language: | English |
| Published: |
Providence, Rhode Island :
American Mathematical Society,
2018.
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| Series: | Memoirs of the American Mathematical Society ;
no. 1215. |
| Subjects: |
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.