Matches in SemOpenAlex for { <https://semopenalex.org/work/W1498754945> ?p ?o ?g. }
- W1498754945 abstract "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 the group, and groups acting on infinite-dimensional hyperbolic space. Moreover, in addition to providing much greater generality than any prior work, 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." @default.
- W1498754945 created "2016-06-24" @default.
- W1498754945 creator A5024503738 @default.
- W1498754945 creator A5048462829 @default.
- W1498754945 creator A5090428395 @default.
- W1498754945 date "2013-01-23" @default.
- W1498754945 modified "2023-09-27" @default.
- W1498754945 title "Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces (extended version)" @default.
- W1498754945 cites W1488440499 @default.
- W1498754945 cites W1590116484 @default.
- W1498754945 cites W1651631132 @default.
- W1498754945 cites W1966848242 @default.
- W1498754945 cites W1968053313 @default.
- W1498754945 cites W1978155691 @default.
- W1498754945 cites W1983774070 @default.
- W1498754945 cites W2005649166 @default.
- W1498754945 cites W2011805522 @default.
- W1498754945 cites W2017279581 @default.
- W1498754945 cites W2035293281 @default.
- W1498754945 cites W2044852057 @default.
- W1498754945 cites W2045336066 @default.
- W1498754945 cites W2054451537 @default.
- W1498754945 cites W2056448004 @default.
- W1498754945 cites W2057975853 @default.
- W1498754945 cites W2059555371 @default.
- W1498754945 cites W2061096368 @default.
- W1498754945 cites W2070649011 @default.
- W1498754945 cites W2081385600 @default.
- W1498754945 cites W2087753479 @default.
- W1498754945 cites W2091151350 @default.
- W1498754945 cites W2091957862 @default.
- W1498754945 cites W2112393190 @default.
- W1498754945 cites W2117968368 @default.
- W1498754945 cites W2133555129 @default.
- W1498754945 cites W2134086356 @default.
- W1498754945 cites W2135961131 @default.
- W1498754945 cites W2149057882 @default.
- W1498754945 cites W2171358215 @default.
- W1498754945 cites W2315250237 @default.
- W1498754945 cites W293955060 @default.
- W1498754945 cites W2962794697 @default.
- W1498754945 cites W2964168273 @default.
- W1498754945 cites W60399575 @default.
- W1498754945 hasPublicationYear "2013" @default.
- W1498754945 type Work @default.
- W1498754945 sameAs 1498754945 @default.
- W1498754945 citedByCount "3" @default.
- W1498754945 countsByYear W14987549452015 @default.
- W1498754945 countsByYear W14987549452016 @default.
- W1498754945 countsByYear W14987549452017 @default.
- W1498754945 crossrefType "posted-content" @default.
- W1498754945 hasAuthorship W1498754945A5024503738 @default.
- W1498754945 hasAuthorship W1498754945A5048462829 @default.
- W1498754945 hasAuthorship W1498754945A5090428395 @default.
- W1498754945 hasConcept C102966492 @default.
- W1498754945 hasConcept C129671197 @default.
- W1498754945 hasConcept C134306372 @default.
- W1498754945 hasConcept C138885662 @default.
- W1498754945 hasConcept C151201525 @default.
- W1498754945 hasConcept C162324750 @default.
- W1498754945 hasConcept C165818556 @default.
- W1498754945 hasConcept C167150821 @default.
- W1498754945 hasConcept C176217482 @default.
- W1498754945 hasConcept C177148314 @default.
- W1498754945 hasConcept C178790620 @default.
- W1498754945 hasConcept C185592680 @default.
- W1498754945 hasConcept C198043062 @default.
- W1498754945 hasConcept C202444582 @default.
- W1498754945 hasConcept C206352148 @default.
- W1498754945 hasConcept C206530611 @default.
- W1498754945 hasConcept C21547014 @default.
- W1498754945 hasConcept C2778572836 @default.
- W1498754945 hasConcept C2781311116 @default.
- W1498754945 hasConcept C33923547 @default.
- W1498754945 hasConcept C40020168 @default.
- W1498754945 hasConcept C41895202 @default.
- W1498754945 hasConcept C49527426 @default.
- W1498754945 hasConcept C51337361 @default.
- W1498754945 hasConcept C68363185 @default.
- W1498754945 hasConcept C70984080 @default.
- W1498754945 hasConcept C73373263 @default.
- W1498754945 hasConcept C83677898 @default.
- W1498754945 hasConcept C92047909 @default.
- W1498754945 hasConceptScore W1498754945C102966492 @default.
- W1498754945 hasConceptScore W1498754945C129671197 @default.
- W1498754945 hasConceptScore W1498754945C134306372 @default.
- W1498754945 hasConceptScore W1498754945C138885662 @default.
- W1498754945 hasConceptScore W1498754945C151201525 @default.
- W1498754945 hasConceptScore W1498754945C162324750 @default.
- W1498754945 hasConceptScore W1498754945C165818556 @default.
- W1498754945 hasConceptScore W1498754945C167150821 @default.
- W1498754945 hasConceptScore W1498754945C176217482 @default.
- W1498754945 hasConceptScore W1498754945C177148314 @default.
- W1498754945 hasConceptScore W1498754945C178790620 @default.
- W1498754945 hasConceptScore W1498754945C185592680 @default.
- W1498754945 hasConceptScore W1498754945C198043062 @default.
- W1498754945 hasConceptScore W1498754945C202444582 @default.
- W1498754945 hasConceptScore W1498754945C206352148 @default.
- W1498754945 hasConceptScore W1498754945C206530611 @default.
- W1498754945 hasConceptScore W1498754945C21547014 @default.