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

By Alan Haynes

Appears in collection : Jean-Morlet chair: Tiling and recurrence / Chaire Jean-Morlet : Pavages et récurrence

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.

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Citation data

  • DOI 10.24350/CIRM.V.19250803
  • Cite this video Haynes, Alan (07/12/2017). Bounded remainder sets for rotations on $p$-adic solenoids. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19250803
  • URL https://dx.doi.org/10.24350/CIRM.V.19250803


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