Orbit Representations from Linear mod 1 Transformations

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2012
• Hauptverfasser: Correia Ramos, C., Martins, N., Pinto, P.R.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2012
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/148466
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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.

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...