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. ISSN 0024-6093

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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
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 24 Jul 2019 18:09
URI: https://ueaeprints.uea.ac.uk/id/eprint/18602
DOI: 10.1112/S0024609397003330

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