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• W2113291246 abstract "We discuss a number of naturally arising problems in arithmetic, culled from completely unrelated sources, which turn out to have a common formulation involving thin orbits. These include the local-global problem for integral Apollonian gaskets and Zaremba's Conjecture on finite continued fractions with absolutely bounded partial quotients. Though these problems could have been posed by the ancient Greeks, recent progress comes from a pleasant synthesis of modern techniques from a variety of fields, including harmonic analysis, algebra, geometry, combinatorics, and dynamics. We describe the problems, partial progress, and some of the tools alluded to above." @default.
• W2113291246 created "2016-06-24" @default.
• W2113291246 creator A5016383096 @default.
• W2113291246 date "2012-08-27" @default.
• W2113291246 modified "2023-09-27" @default.
• W2113291246 title "From Apollonius To Zaremba: Local-Global Phenomena in Thin Orbits" @default.
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• W2113291246 hasPublicationYear "2012" @default.
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