Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces /

"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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Fishman, Lior, 1964- (Autor), Simmons, David, 1988- (Autor), Urbański, Mariusz (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island : American Mathematical Society, 2018.
Colección:Memoirs of the American Mathematical Society ; no. 1215.
Temas:
Diophantine approximation.
Geometry, Hyperbolic.
Hyperbolic spaces.
Metric spaces.
Approximation diophantienne.
Géométrie hyperbolique.
Espaces hyperboliques.
Espaces métriques.
MATHEMATICS > Algebra > Intermediate.
Espacios métricos
Ecuaciones diferenciales hiperbólicas-Soluciones numéricas
Análisis diofántico
Diophantine approximation
Geometry, Hyperbolic
Hyperbolic spaces
Metric spaces
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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