Cookies

We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.


Durham Research Online
You are in:

Orbit-counting in non-hyperbolic dynamical systems.

Everest, G. and Miles, R. and 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.

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
Full text:PDF - Published Version (229Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1515/CRELLE.2007.056
Record Created:18 Oct 2012 15:50
Last Modified:14 Dec 2012 12:08

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitterExport: EndNote, Zotero | BibTex
Usage statisticsLook up in GoogleScholar | Find in a UK Library