T. Ward
An uncountable family of group automorphisms, and a typical member
Ward, T.
Authors
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.
Citation
Ward, T. (1997). An uncountable family of group automorphisms, and a typical member. Bulletin of the London Mathematical Society, 29(5), 577-584. https://doi.org/10.1112/s0024609397003330
Journal Article Type | Article |
---|---|
Publication Date | Sep 1, 1997 |
Deposit Date | Oct 12, 2012 |
Publicly Available Date | Oct 17, 2012 |
Journal | Bulletin of the London Mathematical Society |
Print ISSN | 0024-6093 |
Electronic ISSN | 1469-2120 |
Publisher | Wiley |
Peer Reviewed | Peer Reviewed |
Volume | 29 |
Issue | 5 |
Pages | 577-584 |
DOI | https://doi.org/10.1112/s0024609397003330 |
Public URL | https://durham-repository.worktribe.com/output/1472936 |
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Copyright 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
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