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Rates of Recurrence for Z q and R q Extensions of Subshifts of Finite Type

1994; Wiley; Volume: 49; Issue: 2 Linguagem: Inglês

10.1112/jlms/49.2.401

1469-7750

Mark Pollicott, Richard Sharp,

Mathematical functions and polynomials

Journal of the London Mathematical SocietyVolume 49, Issue 2 p. 401-416 Notes and Papers Rates of Recurrence for Zq and Rq Extensions of Subshifts of Finite Type Mark Pollicott, Mark Pollicott INIC - Centro de Matematica, Faculdade de Ciencias, Praca Gomes Teixeira, 4000 Porto, Portugal and Department of Mathematics, Warwick University, Coventry CV4 7ALSearch for more papers by this authorRichard Sharp, Richard Sharp IHES, 35 Route de Chartres, 91440 Bures sur Yvette, France and School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London El 4NSSearch for more papers by this author Mark Pollicott, Mark Pollicott INIC - Centro de Matematica, Faculdade de Ciencias, Praca Gomes Teixeira, 4000 Porto, Portugal and Department of Mathematics, Warwick University, Coventry CV4 7ALSearch for more papers by this authorRichard Sharp, Richard Sharp IHES, 35 Route de Chartres, 91440 Bures sur Yvette, France and School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London El 4NSSearch for more papers by this author First published: April 1994 https://doi.org/10.1112/jlms/49.2.401Citations: 14AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract In this note we give new asymptotic formulae for certain counting functions associated to the periodic behaviour of Zq and Rq extensions of subshifts of finite type. In the case of the Zq extensions, these strengthen previous estimates of Marcus and Tuncel [9]. For both types of extension, our results complement the central limit type results of Lalley [6]. Our proof requires the application of ideas from thermodynamic formalism. Whilst developing this approach, in Section 2, we take the opportunity to present a counter-example to a related conjecture of Coelho-Filho [2]. Citing Literature Volume49, Issue2April 1994Pages 401-416 RelatedInformation