Orbit Representations from Linear mod 1 Transformations

We show that every point x0∈[0,1] carries a representation of a C∗-algebra that encodes the orbit structure of the linear mod 1 interval map fβ,α(x)=βx+α. Such C∗-algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map fβ,α. Then we prove that s...

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Дата:2012
Автори: Correia Ramos, C., Martins, N., Pinto, P.R.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2012
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/148466
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Orbit Representations from Linear mod 1 Transformations / C. Correia Ramos, N. Martins, P.R. Pinto // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 17 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1484662019-02-19T01:31:14Z Orbit Representations from Linear mod 1 Transformations Correia Ramos, C. Martins, N. Pinto, P.R. We show that every point x0∈[0,1] carries a representation of a C∗-algebra that encodes the orbit structure of the linear mod 1 interval map fβ,α(x)=βx+α. Such C∗-algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map fβ,α. Then we prove that such representation is irreducible. Moreover two such of representations are unitarily equivalent if and only if the points belong to the same generalized orbit, for every α∈[0,1[ and β≥1. 2012 Article Orbit Representations from Linear mod 1 Transformations / C. Correia Ramos, N. Martins, P.R. Pinto // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 46L55; 37B10; 46L05 DOI: http://dx.doi.org/10.3842/SIGMA.2012.029 http://dspace.nbuv.gov.ua/handle/123456789/148466 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description We show that every point x0∈[0,1] carries a representation of a C∗-algebra that encodes the orbit structure of the linear mod 1 interval map fβ,α(x)=βx+α. Such C∗-algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map fβ,α. Then we prove that such representation is irreducible. Moreover two such of representations are unitarily equivalent if and only if the points belong to the same generalized orbit, for every α∈[0,1[ and β≥1.
format Article
author Correia Ramos, C.
Martins, N.
Pinto, P.R.
spellingShingle Correia Ramos, C.
Martins, N.
Pinto, P.R.
Orbit Representations from Linear mod 1 Transformations
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Correia Ramos, C.
Martins, N.
Pinto, P.R.
author_sort Correia Ramos, C.
title Orbit Representations from Linear mod 1 Transformations
title_short Orbit Representations from Linear mod 1 Transformations
title_full Orbit Representations from Linear mod 1 Transformations
title_fullStr Orbit Representations from Linear mod 1 Transformations
title_full_unstemmed Orbit Representations from Linear mod 1 Transformations
title_sort orbit representations from linear mod 1 transformations
publisher Інститут математики НАН України
publishDate 2012
url http://dspace.nbuv.gov.ua/handle/123456789/148466
citation_txt Orbit Representations from Linear mod 1 Transformations / C. Correia Ramos, N. Martins, P.R. Pinto // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 17 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT correiaramosc orbitrepresentationsfromlinearmod1transformations
AT martinsn orbitrepresentationsfromlinearmod1transformations
AT pintopr orbitrepresentationsfromlinearmod1transformations
first_indexed 2023-05-20T17:30:45Z
last_indexed 2023-05-20T17:30:45Z
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