Orbit Representations from Linear mod 1 Transformations

• Author(s): Ramos, Carlos Correia ; Martins, Nuno ; Pinto, Paulo R.
• Date: 2012
• Persistent ID: http://hdl.handle.net/10174/7927
• Origin: Repositório Científico da Universidade de Évora
• Subject(s): interval maps; symbolic dynamics; C -algebras; representations of algebras
• Document Type: Article
• Language: English
• Editor(s): Nikitin, Anatoly

Description

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.