Orbit-counting in non-hyperbolic dynamical systems

Everest, G, Miles, R, Stevens, S and Ward, T (2007) Orbit-counting in non-hyperbolic dynamical systems. Journal für die reine und angewandte Mathematik (Crelles Journal), 2007 (608). pp. 155-182. ISSN 0075-4102

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Abstract

There are well-known analogs of the prime number theorem and Mertens' theorem for dynamical systems with hyperbolic behaviour. Here we consider the same question for the simplest non-hyperbolic algebraic systems. The asymptotic behaviour of the orbit-counting function is governed by a rotation on an associated compact group, and in simple examples we exhibit uncountably many different asymptotic growth rates for the orbit-counting function. Mertens' Theorem also holds in this setting, with an explicit rational leading coefficient obtained from arithmetic properties of the non-hyperbolic eigendirections.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:44
Last Modified: 24 Jul 2019 15:29
URI: https://ueaeprints.uea.ac.uk/id/eprint/19746
DOI: 10.1515/CRELLE.2007.056

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