## 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.

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.

Original language | English |
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Title of host publication | Series: Mathematical Modelling in Physics, Engineering and Cognitive Science. |

Editors | Andrei Khrennikov |

Publisher | Växjö University Press |

Pages | 109-143 |

Number of pages | 35 |

Volume | 6 |

ISBN (Print) | 91-7636-386-4 |

Publication status | Published - 2003 |

Event | Workshop Dynamical Systems from Number Theory to Probability 2 - Växjö University, Växjö, Sweden Duration: 2002 Dec 6 → … |

### Publication series

Name | |
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Volume | 6 |

ISSN (Print) | 1651-0267 |

### Conference

Conference | Workshop Dynamical Systems from Number Theory to Probability 2 |
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Country/Territory | Sweden |

City | Växjö University, Växjö |

Period | 2002/12/06 → … |

## Subject classification (UKÄ)

- Mathematics