Automorphisms with exotic orbit growth

• Autorzy: Stephan Baier , Sawian Jaidee , Shaun Stevens , Thomas Ward
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 37P35: Arithmetic properties of periodic points
• 37C35: Orbit growth

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 158
• Numer: 2
• Strony: 173-197

Daty

wydano

2013

Twórcy

autor

Stephan Baier

• School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK

autor

Sawian Jaidee

• Department of Mathematics, 123 Mittraphab Road, Khon Kaen 40002, Thailand

autor

Shaun Stevens

• School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK

autor

Thomas Ward

• Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK

Identyfikatory

DOI

10.4064/aa158-2-5