Synchronization points and associated dynamical invariants

MILES, Richard (2013). Synchronization points and associated dynamical invariants. Transactions of the American Mathematical Society (TRAN), 365, 5503-5524.

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Official URL: https://doi.org/10.1090/S0002-9947-2013-05829-1
Link to published version:: 10.1090/S0002-9947-2013-05829-1

Abstract

This paper introduces new invariants for multiparameter dynamical systems. This is done by counting the number of points whose orbits intersect at time n under simultaneous iteration of finitely many endomorphisms. We call these points synchronization points. The resulting sequences of counts together with generating functions and growth rates are subsequently investigated for homeomorphisms of compact metric spaces, toral automorphisms and compact abelian group epimorphisms. Synchronization points are also used to generate invariant measures and the distribution properties of these are analysed for the algebraic systems considered. Furthermore, these systems reveal strong connections between the new invariants and problems of active interest in number theory, relating to heights and greatest common divisors

Item Type: Article
Departments: Development and Society > Teacher Education
Identification Number: 10.1090/S0002-9947-2013-05829-1
Depositing User: Richard Miles
Date Deposited: 26 Jan 2018 15:38
Last Modified: 26 Jan 2018 15:38
URI: http://shura.shu.ac.uk/id/eprint/17224

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