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AN UNCOUNTABLE FAMILY OF GROUP AUTOMORPHISMS, AND A TYPICAL MEMBER

Published online by Cambridge University Press:  01 September 1997

THOMAS WARD
THOMAS WARD
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ
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Abstract

We describe an uncountable family of compact group automorphisms with entropy log 2. 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 log 2, and lower growth rate equal to zero.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 5 , September 1997 , pp. 577 - 584
Copyright
© The London Mathematical Society 1997

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