Automorphisms with exotic orbit growth

Baier, Stephan, Jaidee, Sawian, Stevens, Shaun and Ward, Tom (2013) Automorphisms with exotic orbit growth. Acta Arithmetica, 158. pp. 173-197. ISSN 0065-1036

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Abstract

The dynamical Mertens' theorem describes asymptotics for the growth in the number of closed orbits in a dynamical system. We construct families of ergodic automorphisms of fixed entropy on compact connected groups with a continuum of growth rates on two different growth scales. This shows in particular that the space of all ergodic algebraic dynamical systems modulo the equivalence of shared orbit-growth asymptotics is not countable. In contrast, for the equivalence relation of measurable isomorphism or equal entropy it is not known if the quotient space is countable or uncountable (this problem is a manifestation of Lehmer's problem).

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
University of East Anglia > Faculty of Science > Research Groups > Number Theory
University of East Anglia > Faculty of Science > Research Groups > Algebra and Combinatorics
Depositing User: Pure Connector
Date Deposited: 07 Sep 2013 06:13
Last Modified: 25 Jul 2018 08:34
URI: https://ueaeprints.uea.ac.uk/id/eprint/43217
DOI: 10.4064/aa158-2-5

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