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SKEW-PRODUCT DYNAMICAL SYSTEMS, ELLIS GROUPS AND TOPOLOGICAL CENTRE

Part of: Abstract harmonic analysis Ergodic theory

Published online by Cambridge University Press:  09 February 2009

A. JABBARI  and
H. R. E. VISHKI
A. JABBARI*
Affiliation:
Department of Mathematics, Ferdowsi University, PO Box 1159, Mashhad 91775, Iran (email: shahzadeh@math.um.ac.ir)
H. R. E. VISHKI
Affiliation:
Department of Mathematics, Ferdowsi University, PO Box 1159, Mashhad 91775, Iran Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Iran (email: vishki@ferdowsi.um.ac.ir)
*
✉For correspondence; e-mail: shahzadeh@math.um.ac.ir
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Abstract

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In this paper, a general construction of a skew-product dynamical system, for which the skew-product dynamical system studied by Hahn is a special case, is given. Then the ergodic and topological properties (of a special type) of our newly defined systems (called Milnes-type systems) are investigated. It is shown that the Milnes-type systems are actually natural extensions of dynamical systems corresponding to some special distal functions. Finally, the topological centre of Ellis groups of any skew-product dynamical system is calculated.

Keywords

flowminimal flowdistal flowuniquely ergodic flowEllis groupcompact right topological grouptopological centre

MSC classification

Secondary: 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions 37A05: Measure-preserving transformations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 1 , February 2009 , pp. 129 - 145
Copyright
Copyright © Australian Mathematical Society 2009

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