Orbit-counting in non-hyperbolic dynamical systems

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dc.creatorEverest, G.
dc.creatorMiles, R.
dc.creatorStevens, S.
dc.creatorWard, T.
dc.date2005-11-22
dc.date.accessioned2026-07-07T08:30:56Z
dc.date.available2026-07-07T08:30:56Z
dc.descriptionThere 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.
dc.identifierhttps://arxiv.org/abs/math/0511569
dc.identifierhttp://arxiv.org/abs/math/0511569
dc.identifierJournal fÃ1/4r die reine und angewandte Mathematik, 608, 155-182, 2007
dc.identifierdoi:10.1515/CRELLE.2007.056
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138370
dc.subjectDynamical Systems
dc.subjectNumber Theory
dc.subject37C30; 26E30; 12J25
dc.titleOrbit-counting in non-hyperbolic dynamical systems
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