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From dynamical systems to commutativity in non-commutative operator algebras

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Author

Editor

  • Andrei Khrennikov

Summary, in English

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.

Department/s

Publishing year

2003

Language

English

Pages

109-143

Publication/Series

Series: Mathematical Modelling in Physics, Engineering and Cognitive Science.

Volume

6

Document type

Conference paper

Publisher

Växjö University Press

Topic

  • Mathematics

Conference name

Workshop Dynamical Systems from Number Theory to Probability 2

Conference date

2002-12-06

Conference place

Växjö University, Växjö, Sweden

Status

Published

Project

  • Non-commutative Analysis of Dynamics, Fractals and Wavelets

Research group

  • Non-commutative Geometry
  • Dynamical systems

ISBN/ISSN/Other

  • ISSN: 1651-0267
  • ISBN: 91-7636-386-4