Rigidity times for a weakly mixing dynamical system which are not rigidity times for any irrational rotation

Bassam Fayad; Adam Kanigowski

doi:10.1017/etds.2014.40

Rigidity times for a weakly mixing dynamical system which are not rigidity times for any irrational rotation

Bassam Fayad
, Adam Kanigowski

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We construct an increasing sequence of natural numbers with the property that is dense in for any , and a continuous measure on the circle such that . Moreover, for every fixed , the set is infinite. This is a sufficient condition for the existence of a rigid, weakly mixing dynamical system whose rigidity time is not a rigidity time for any system with a discrete part in its spectrum.

Original language	English (US)
Pages (from-to)	2529-2534
Number of pages	6
Journal	Ergodic Theory and Dynamical Systems
Volume	35
Issue number	8
DOIs	https://doi.org/10.1017/etds.2014.40
State	Published - Aug 4 2015

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1017/etds.2014.40

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abstract = "We construct an increasing sequence of natural numbers with the property that is dense in for any , and a continuous measure on the circle such that . Moreover, for every fixed , the set is infinite. This is a sufficient condition for the existence of a rigid, weakly mixing dynamical system whose rigidity time is not a rigidity time for any system with a discrete part in its spectrum.",

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AU - Fayad, Bassam

AU - Kanigowski, Adam

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PY - 2015/8/4

Y1 - 2015/8/4

N2 - We construct an increasing sequence of natural numbers with the property that is dense in for any , and a continuous measure on the circle such that . Moreover, for every fixed , the set is infinite. This is a sufficient condition for the existence of a rigid, weakly mixing dynamical system whose rigidity time is not a rigidity time for any system with a discrete part in its spectrum.

AB - We construct an increasing sequence of natural numbers with the property that is dense in for any , and a continuous measure on the circle such that . Moreover, for every fixed , the set is infinite. This is a sufficient condition for the existence of a rigid, weakly mixing dynamical system whose rigidity time is not a rigidity time for any system with a discrete part in its spectrum.

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UR - https://www.scopus.com/pages/publications/84949317275#tab=citedBy

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DO - 10.1017/etds.2014.40

M3 - Article

AN - SCOPUS:84949317275

SN - 0143-3857

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JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 8

ER -

Rigidity times for a weakly mixing dynamical system which are not rigidity times for any irrational rotation

Abstract

All Science Journal Classification (ASJC) codes

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