An uncountable family of group automorphisms, and a typical member

Ward, T.

doi:10.1112/s0024609397003330

An uncountable family of group automorphisms, and a typical member

Ward, T.

Authors

T. Ward

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

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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