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An uncountable family of group automorphisms, and a typical member.

Ward, T. (1997) 'An uncountable family of group automorphisms, and a typical member.', Bulletin of the London Mathematical Society., 29 (5). pp. 577-584.

Abstract

We describe an uncountable family of compact group automorphisms with entropy log2. Each member of the family has a distinct dynamical zeta function, and the members are parametrised by a probability space. A positive proportion of the members have positive upper growth rate of periodic points, and almost all of them have an irrational dynamical zeta function. If infinitely many Mersenne numbers have a bounded number of prime divisors, then a typical member of the family has upper growth rate of periodic points equal to log2, and lower growth rate equal to zero.

Item Type:Article
Full text:PDF - Accepted Version (170Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1112/S0024609397003330
Publisher statement:This is a pre-copy-editing author-produced PDF of an article accepted for publication in Bulletin of the London Mathematical Society following peer review. The definitive publisher-authenticated version Ward, T. (1997) 'An uncountable family of group automorphisms, and a typical member.', Bulletin of the London Mathematical Society., 29 (5). pp. 577-584 is available online at: http://dx.doi.org/10.1112/S0024609397003330
Record Created:12 Oct 2012 13:05
Last Modified:17 Oct 2012 10:43

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