Piecewise contractions are asymptotically periodic
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- by Henk Bruin and Jonathan H. B. Deane PDF
- Proc. Amer. Math. Soc. 137 (2009), 1389-1395 Request permission
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.References
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Additional Information
- Henk Bruin
- Affiliation: Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom
- MR Author ID: 329851
- 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
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1389-1395
- MSC (2000): Primary 37E99, 37C70, 37N99
- DOI: https://doi.org/10.1090/S0002-9939-08-09633-0
- MathSciNet review: 2465664