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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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Інститут математики НАН України
2012
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/148466 |
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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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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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 |
| _version_ |
1796153459214385152 |