An uncountable family of group automorphisms, and a typical member

Ward, Thomas (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

Preview

PDF (family.pdf) - Accepted Version Download (188kB) | Preview

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
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 14:48
Last Modified:	10 Jan 2024 01:26
URI:	https://ueaeprints.uea.ac.uk/id/eprint/18602
DOI:	10.1112/S0024609397003330

Downloads

Actions (login required)

View Item