An Uncountable Family of Group Automorphisms, and a Typical Member

T Ward

Research output: Contribution to journalArticle

11 Citations (Scopus)
3 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)577-584
Number of pages8
JournalBulletin of the London Mathematical Society
Volume29
Issue number5
DOIs
Publication statusPublished - 1997

Cite this