Periodicity and recurrence in piecewise rotations of Eucledian spaces
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Mendes, Miguel and Nicol, Matthew (2004) Periodicity and recurrence in piecewise rotations of Eucledian spaces International Journal of Bifurcation and Chaos, 14 . pp. 2353-2361.
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Abstract
We consider the behavior of piecewise isometries in Euclidean spaces. We show that if n is odd and the system contains no orientation reversing isometries then recurrent orbits with rational coding are not expected. More precisely, a prevalent set of piecewise isometries do not have recurrent points having rational coding. This implies that when all atoms are convex no periodic points exist for almost every piecewise isometry.
By contrast, if n equal to or greater than 2 is even then periodic points are stable for almost every piecewise isometry whose set of defining isometries are not orientation reversing. If, in addition, the defining isometries satisfy an incommensurability condition then all unbounded orbits must be irrationally coded.
| Item Type: | Article |
|---|---|
| Additional Information: | Published in International Journal of Bifurcation and Chaos, 14, 2353-2361. © 2004 World Scientific Publishing. Click here to access the published version. |
| Uncontrolled Keywords: | Piecewise isometries, Euclidean group, recurrence, periodic points |
| Divisions: | Faculty of Engineering and Physical Sciences > Mathematics |
| ID Code: | 1385 |
| Deposited By: | Mr Adam Field |
| Deposited On: | 27 May 2010 15:40 |
| Last Modified: | 28 Sep 2012 10:50 |
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