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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Piecewise contractions are asymptotically periodic


Authors: Henk Bruin and Jonathan H. B. Deane
Journal: Proc. Amer. Math. Soc. 137 (2009), 1389-1395
MSC (2000): Primary 37E99, 37C70, 37N99
Published electronically: July 31, 2008
MathSciNet review: 2465664
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Abstract: We show that, given a finite partition of the plane $ \mathbb{C}$ such that the map $ G$ acts as a linear contraction on each part, for almost every choice of parameters every orbit of $ G$ is (asymptotically) periodic.


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Additional Information

Henk Bruin
Affiliation: Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom
Email: H.Bruin@surrey.ac.uk

Jonathan H. B. Deane
Affiliation: Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom
Email: J.Deane@surrey.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09633-0
PII: S 0002-9939(08)09633-0
Keywords: Piecewise contraction, piecewise isometry
Received by editor(s): December 12, 2007
Received by editor(s) in revised form: May 1, 2008
Published electronically: July 31, 2008
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.