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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2012 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862548177273487360 |
|---|---|
| author | Correia Ramos, C. Martins, N. Pinto, P.R. |
| author_facet | Correia Ramos, C. Martins, N. Pinto, P.R. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-25T16:03:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148466 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T16:03:39Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Correia Ramos, C. Martins, N. Pinto, P.R. 2019-02-18T13:25:02Z 2019-02-18T13:25:02Z 2012 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 https://nasplib.isofts.kiev.ua/handle/123456789/148466 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. First author acknowledges CIMA-UE for financial support. The other authors were partially
 supported by the Fundacao para a Ciencia e a Tecnologia through the Program POCI 2010/FEDER. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Orbit Representations from Linear mod 1 Transformations Article published earlier |
| spellingShingle | Orbit Representations from Linear mod 1 Transformations Correia Ramos, C. Martins, N. Pinto, P.R. |
| title | 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_short | Orbit Representations from Linear mod 1 Transformations |
| title_sort | orbit representations from linear mod 1 transformations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148466 |
| work_keys_str_mv | AT correiaramosc orbitrepresentationsfromlinearmod1transformations AT martinsn orbitrepresentationsfromlinearmod1transformations AT pintopr orbitrepresentationsfromlinearmod1transformations |