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H 2 Bounded remainder sets for rotations on $p$-adic solenoids

Auteurs : Haynes, Alan (Auteur de la Conférence)
CIRM (Editeur )

 Loading the player... bounded remainder sets Diophantine approximation rotations on compact groups uniform distribution discrepancy theory connected compact abelian groups adeles $p$-adic numbers $p$-adic solenoids dynamical coboundaries cut and project sets $p$-adic internal spaces

Résumé : 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.

Codes MSC :
11J71 - Distribution modulo one
11K06 - General theory of distribution modulo 1
11K38 - Irregularities of distribution, discrepancy

 Informations sur la Vidéo Langue : Anglais Date de publication : 08/12/2017 Date de captation : 07/12/2017 Collection : Research talks ; Number Theory Format : MP4 (.mp4) - HD Durée : 00:59:58 Domaine : Number Theory Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2017-12-07_Haynes.mp4 Informations sur la rencontre Nom de la rencontre : Jean-Morlet chair: Tiling and recurrence / Chaire Jean-Morlet : Pavages et récurrenceOrganisateurs de la rencontre : Akiyama, Shigeki ; Arnoux, PierreDates : 04/12/2017 - 08/12/2017 Année de la rencontre : 2017 URL Congrès : https://akiyama-arnoux.weebly.com/conference.html Citation Data DOI : 10.24350/CIRM.V.19250803 Cite 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

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