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Bounded remainder sets for rotations on $p$-adic solenoids
Post-edited
Authors : Haynes, Alan (Author of the conference)
CIRM (Publisher )
11J71 - Distribution modulo one
11K06 - General theory of distribution modulo 1
11K38 - Irregularities of distribution, discrepancy
CIRM (Publisher )
Abstract :
Bounded remainder sets for a dynamical system are sets for which the Birkhoff averages of return times differ from the expected values by at most a constant amount. These sets are rare and important objects which have been studied for over 100 years. In the last few years there have been a number of results which culminated in explicit constructions of bounded remainder sets for toral rotations in any dimension, of all possible allowable volumes. In this talk we are going to explain these results, and then explain how to generalize them to give explicit constructions of bounded remainder sets for rotations in $p$-adic solenoids. Our method of proof will make use of a natural dynamical encoding of patterns in non-Archimedean cut and project sets.
MSC Codes : 11J71 - Distribution modulo one
11K06 - General theory of distribution modulo 1
11K38 - Irregularities of distribution, discrepancy
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 08/12/2017 Conference Date : 07/12/2017 Subseries : Research talks arXiv category : Number Theory ; Dynamical Systems Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:59:58 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-12-07_Haynes.mp4 
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Information on the Event
Event Title : Jean-Morlet chair: Tiling and recurrence / Chaire Jean-Morlet : Pavages et récurrenceEvent Organizers : Akiyama, Shigeki ; Arnoux, Pierre Dates : 04/12/2017 - 08/12/2017 Event Year : 2017 Event URL : https://www.chairejeanmorlet.com/1721.html
Citation Data
DOI : 10.24350/CIRM.V.19250803Cite this video as: Haynes, Alan (2017). Bounded remainder sets for rotations on $p$-adic solenoids. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19250803 URI : http://dx.doi.org/10.24350/CIRM.V.19250803 |
See Also
- [Multi angle] Dimension groups and recurrence for tree subshifts / Author of the conference Berthé, Valérie.
- [Multi angle] A perspective on the The Fibonacci trace map / Author of the conference Damanik, David.
- [Multi angle] Yet another characterization of the Pisot conjecture / Author of the conference Mercat, Paul.
- [Multi angle] Algebraic sums and products of univoque bases / Author of the conference Dajani, Karma.
Bibliography
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