From dynamical systems to commutativity in non-commutative operator algebras
Persson, Tomas; Silvestrov, Sergei (2003). From dynamical systems to commutativity in non-commutative operator algebras. Khrennikov, Andrei (Ed.). Series: Mathematical Modelling in Physics, Engineering and Cognitive Science., 6,, 109 - 143. Workshop Dynamical Systems from Number Theory to Probability 2. Växjö University, Växjö, Sweden: Växjö University Press
Conference Proceeding/Paper
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Published
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English
Authors:
Persson, Tomas
;
Silvestrov, Sergei
Editors:
Khrennikov, Andrei
Department:
Mathematics (Faculty of Engineering)
Non-commutative Geometry-lup-obsolete
Dynamical systems
Project:
Non-commutative Analysis of Dynamics, Fractals and Wavelets
Research Group:
Non-commutative Geometry-lup-obsolete
Dynamical systems
Abstract:
This article is devoted to investigation of connection of operator representations of commutation relations
XX*=F(X*X) and AB = BF(A) to periodic points and orbits of the dynamical system generated by the function F. Conditions on the general function F for two monomials in operators A and B to commute are derived. These conditions are further studied for dynamical systems generated by affine and q-deformed power functions, and for the
beta-shift dynamical system.
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