From dynamical systems to commutativity in non-commutative operator algebras

Tomas Persson; Sergei Silvestrov

From dynamical systems to commutativity in non-commutative operator algebras

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

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.

Original language	English
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
Volume	6
ISSN (Print)	1651-0267

Conference

Conference	Workshop Dynamical Systems from Number Theory to Probability 2
Country/Territory	Sweden
City	Växjö University, Växjö
Period	2002/12/06 → …

Subject classification (UKÄ)

Mathematical Sciences

Cite this

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title = "From dynamical systems to commutativity in non-commutative operator algebras",

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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publisher = "V{\"a}xj{\"o} University Press",

pages = "109--143",

editor = "Andrei Khrennikov",

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

note = "Workshop Dynamical Systems from Number Theory to Probability 2 ; Conference date: 06-12-2002",

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Persson, T & Silvestrov, S 2003, From dynamical systems to commutativity in non-commutative operator algebras. in A Khrennikov (ed.), Series: Mathematical Modelling in Physics, Engineering and Cognitive Science.. vol. 6, Växjö University Press, pp. 109-143, Workshop Dynamical Systems from Number Theory to Probability 2, Växjö University, Växjö, Sweden, 2002/12/06.

From dynamical systems to commutativity in non-commutative operator algebras. / Persson, Tomas; Silvestrov, Sergei.
Series: Mathematical Modelling in Physics, Engineering and Cognitive Science.. ed. / Andrei Khrennikov. Vol. 6 Växjö University Press, 2003. p. 109-143.

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

TY - GEN

T1 - From dynamical systems to commutativity in non-commutative operator algebras

AU - Persson, Tomas

AU - Silvestrov, Sergei

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

M3 - Paper in conference proceeding

SN - 91-7636-386-4

VL - 6

SP - 109

EP - 143

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

A2 - Khrennikov, Andrei

PB - Växjö University Press

T2 - Workshop Dynamical Systems from Number Theory to Probability 2

Y2 - 6 December 2002

ER -

From dynamical systems to commutativity in non-commutative operator algebras

Abstract

Publication series

Conference

Subject classification (UKÄ)

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Cite this