Abstract
In this paper we investigate the most basic two-dimensional generalizations of interval exchange maps. The system studied is obtained by composing two rotations. We illustrate a new example of an attractor. The structure of this attractor appears to be present in the invertible piecewise rotation systems with two atoms. In the non-invertible case, we also illustrate a bifurcation mechanism leading to births of satellite systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adler, R., Kitchens, B. and Tresser, C. [1999] Dynamics of nonergodic piecewise affine maps of the toruspreprint.
Ashwin, P., Chambers, W. and Petkov, G. [1997] Lossless digital filter overflow oscillations; approximation of invariant fractals. Inter. Journal of Bifur. and Chaos, Vol. 7, No. 11 2603–2610.
Goetz, A. [1998a] Dynamics of a piecewise rotation, Continuous and Discrete Dynamical Systems, 4 (4) 1998, p. 593–608..
Goetz, A. [1998b] Perturbations of 8-attractors and births of satellite systems, International Journal of Bifurcation and Chaos, Vol 8, No. 10 1937–1956.
Guillaume, P. [2000] Une isom¨¦trie par morceaux sur le toreMarseille University.
Kahng, B. [2000] Ph.D. ThesisUniversity of Illinois at Urbana-Champain.
Melbourne, I., Dellnitz, M. and Golubitsky, M. [1993] The Structure of Symmetric Attractors, Arch. Rational Mech. Anal. 123 75–98.
Mendes, M. [2000] Piecewise Rotations and new concepts of Symmetry and Invariance, PhD Transfer ReportUniversity of Surrey.
Mendes, M. [2001] Quasi-Invariant Attractors of Piecewise Isometric Systemssubmitted for publication.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Basel AG
About this chapter
Cite this chapter
Goetz, A., Mendes, M. (2003). Piecewise Rotations: Bifurcations, Attractors and Symmetries. In: Buescu, J., Castro, S.B.S.D., da Silva Dias, A.P., Labouriau, I.S. (eds) Bifurcation, Symmetry and Patterns. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7982-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7982-8_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9642-9
Online ISBN: 978-3-0348-7982-8
eBook Packages: Springer Book Archive