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Piecewise contractions are asymptotically periodic
Author(s):
Henk
Bruin;
Jonathan
H. B.
Deane
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1389-1395.
MSC (2000):
Primary 37E99, 37C70, 37N99
Posted:
July 31, 2008
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Abstract:
We show that, given a finite partition of the plane  such that the map  acts as a linear contraction on each part, for almost every choice of parameters every orbit of  is (asymptotically) periodic.
References:
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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:
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
Posted:
July 31, 2008
Communicated by:
Jane M. Hawkins
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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