Stephan Baier
Automorphisms with exotic orbit growth
Baier, Stephan; Jaidee, Sawian; Stevens, Shaun; Ward, Thomas
Authors
Sawian Jaidee
Shaun Stevens
Thomas Ward
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).
Citation
Baier, S., Jaidee, S., Stevens, S., & Ward, T. (2013). Automorphisms with exotic orbit growth. Acta Arithmetica, 158, 173-197. https://doi.org/10.4064/aa158-2-5
Journal Article Type | Article |
---|---|
Publication Date | Jan 1, 2013 |
Deposit Date | Feb 28, 2013 |
Publicly Available Date | Apr 17, 2013 |
Journal | Acta Arithmetica |
Print ISSN | 0065-1036 |
Electronic ISSN | 1730-6264 |
Publisher | Instytut Matematyczny |
Peer Reviewed | Peer Reviewed |
Volume | 158 |
Pages | 173-197 |
DOI | https://doi.org/10.4064/aa158-2-5 |
Files
Accepted Journal Article
(372 Kb)
PDF
Copyright Statement
Copyright © 2013 IMPAN. All rights reserved.
You might also like
Directional uniformities, periodic points, and entropy
(2015)
Journal Article
Book review: "Automorphisms and equivalence relations in topological dynamics"
(2015)
Journal Article
Homogeneous dynamics: a study guide
(2015)
Book Chapter
Dynamical invariants for group automorphisms
(2015)
Book Chapter
Towards a Pólya–Carlson dichotomy for algebraic dynamics
(2014)
Journal Article