Periodicity and Recurrence in Piecewise Rotations of Euclidean spaces

• Type: Article in International Scientific Journal
• Date: 2004

Authors

Miguel Ângelo de Sousa Mendes (Author) FEUP; Matthew Nicol (Author) Other

Journal

Title: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Vol. 14 No. 7

Pages: 2353-2360

ISSN: 0218-1274

Publisher: World Scientific

Other information

DOI: 10.1142/S0218127404010813

Abstract (EN): We consider the behaviour 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>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

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 8