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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2018.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1215. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_on1042567167 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
| 007 | cr |n||||||||| | ||
| 008 | 180703t20182018riu ob 000 0 eng d | ||
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| 020 | |a 1470447460 |q (online) | ||
| 020 | |a 9781470447465 |q (electronic bk.) | ||
| 020 | |z 1470428865 |q (print) | ||
| 020 | |z 9781470428860 |q (print) | ||
| 035 | |a (OCoLC)1042567167 | ||
| 050 | 4 | |a QA242 |b .F57 2018 | |
| 072 | 7 | |a MAT |x 002040 |2 bisacsh | |
| 082 | 0 | 4 | |a 512.73 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Fishman, Lior, |d 1964- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjtDj9TckfC7btwDjWBJj3 | |
| 245 | 1 | 0 | |a Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces / |c Lior Fishman, David Simmons, Mariusz Urbański. |
| 264 | 1 | |a Providence, Rhode Island : |b American Mathematical Society, |c 2018. | |
| 264 | 4 | |c ©2018 | |
| 300 | |a 1 online resource (v, 137 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v volume 254, number 1215 | |
| 588 | 0 | |a Print version record. | |
| 500 | |a "July 2018, volume 254, number 1215 (third of 5 numbers)." | ||
| 500 | |a "Keywords: Diophantine approximation, Schmidt's game, hyperbolic geometry, Gromov hyperbolic metric spaces." | ||
| 504 | |a Includes bibliographical references (pages 133-137). | ||
| 520 | 3 | |a "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 Hersonsky and Paulin ('02, '04, '07). Concrete examples of situations we consider which have not been considered before include geometrically infinite Kleinian groups, geometrically finite Kleinian groups where the approximating point is not a fixed point of any element of the group, and groups acting on infinite-dimensional hyperbolic space. Moreover, in addition to providing much greater generality than any prior work of which we are aware, our results also give new insight into the nature of the connection between Diophantine approximation and the geometry of the limit set within which it takes place. Two results are also contained here which are purely geometric: a generalization of a theorem of Bishop and Jones ('97) to Gromov hyperbolic metric spaces, and a proof that the uniformly radial limit set of a group acting on a proper geodesic Gromov hyperbolic metric space has zero Patterson-Sullivan measure unless the group is quasiconvex-cocompact. The latter is an application of a Diophantine theorem." |c Provided by publisher | |
| 505 | 0 | |a 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. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Diophantine approximation. | |
| 650 | 0 | |a Geometry, Hyperbolic. | |
| 650 | 0 | |a Hyperbolic spaces. | |
| 650 | 0 | |a Metric spaces. | |
| 650 | 6 | |a Approximation diophantienne. | |
| 650 | 6 | |a Géométrie hyperbolique. | |
| 650 | 6 | |a Espaces hyperboliques. | |
| 650 | 6 | |a Espaces métriques. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Espacios métricos |2 embne | |
| 650 | 0 | 7 | |a Ecuaciones diferenciales hiperbólicas-Soluciones numéricas |2 embucm |
| 650 | 0 | 7 | |a Análisis diofántico |2 embucm |
| 650 | 7 | |a Diophantine approximation |2 fast | |
| 650 | 7 | |a Geometry, Hyperbolic |2 fast | |
| 650 | 7 | |a Hyperbolic spaces |2 fast | |
| 650 | 7 | |a Metric spaces |2 fast | |
| 700 | 1 | |a Simmons, David, |d 1988- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjF4gR6qWVp7DgCwxXvv9C | |
| 700 | 1 | |a Urbański, Mariusz, |e author. | |
| 710 | 2 | |a American Mathematical Society, |e publisher. | |
| 776 | 0 | 8 | |i Print version: |a FISHMAN, LIOR. |t DIOPHANTINE APPROXIMATION AND THE GEOMETRY OF LIMIT SETS IN GROMOV HYPERBOLIC METRIC SPACES. |d [S.l.] : AMER MATHEMATICAL SOCIETY, 2018 |z 1470428865 |w (OCoLC)1031536263 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1215. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5501869 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37445185 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL5501869 | ||
| 938 | |a EBSCOhost |b EBSC |n 1879714 | ||
| 938 | |a YBP Library Services |b YANK |n 15675528 | ||
| 994 | |a 92 |b IZTAP | ||