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# Documents  Haynes, Alan | enregistrements trouvés : 2

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## Bounded remainder sets for rotations on $p$-adic solenoids Haynes, Alan | CIRM H

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Number Theory

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. 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 ...

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## Sums of reciprocals of fractional parts and multiplicative diophantine approximation Beresnevich, Victor ; Haynes, Alan ; Velani, Sanju | American Mathematical Society 2020

Ouvrage

- vii; 77 p.
ISBN 978-1-4704-4095-4

Memoirs of the American Mathematical Society , 1276

Localisation : Collection 1er étage

approximation diophantienne multiplicative # expansion d'Ostrowski # distribution uniforme

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