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Title: Orbit Representations from Linear mod 1 Transformations
Authors: Ramos, Carlos Correia
Martins, Nuno
Pinto, Paulo R.
Editors: Nikitin, Anatoly
Keywords: interval maps
symbolic dynamics
C -algebras
representations of algebras
Issue Date: 16-May-2012
Publisher: Department of Applied Research, Institute of Mathematics of National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka Street, Kyiv 4, 01601 Ukraine
Citation: Correia Ramos, Carlos; Martins, Nuno; Pinto, Paulo R. Orbit representations from linear mod 1 transformations. SIGMA Symmetry Integrability Geom. Methods Appl. 8 (2012), Paper 029, 9 pp.
Abstract: 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.
Type: article
Appears in Collections:MAT - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica
CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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