Orbit Representations from Linear mod 1 Transformations
We show that every point x0 2 [0; 1] carries a representation of a C -algebra that encodes the orbit structure of the linear mod 1 interval map f ; (x) = x + . Such C -algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map f ; . Then we prove t...
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| Outros Autores: | , |
| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2013
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| Assuntos: | |
| Texto completo: | http://hdl.handle.net/10174/7927 |
| País: | Portugal |
| Oai: | oai:dspace.uevora.pt:10174/7927 |
| Resumo: | We show that every point x0 2 [0; 1] carries a representation of a C -algebra that encodes the orbit structure of the linear mod 1 interval map f ; (x) = x + . Such C -algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map f ; . 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 2 [0; 1[ and 1. |
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