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Periodicity and recurrence in piecewise rotations of Eucledian spaces

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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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
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Mendes, Miguel
Nicol, Matthew
Date : 1 July 2004
Uncontrolled Keywords : Piecewise isometries, Euclidean group, recurrence, periodic points
Additional Information : Published in International Journal of Bifurcation and Chaos, 14, 2353-2361. © 2004 World Scientific Publishing. Click here to access the published version.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:40
Last Modified : 31 Oct 2017 14:01

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