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Dynamics of a family of piecewise-linear area-preserving plane maps I. Rational rotation numbers.
- Source :
-
Journal of Difference Equations & Applications . Oct2005, Vol. 11 Issue 12, p1089-1108. 20p. - Publication Year :
- 2005
-
Abstract
- This paper studies the behavior under iteration of the maps Tab(x, y) = (Fab(x) - y, x) of the plane R², in which Fab(x) = ax if x ≥ 0 and bx if x « 0. The orbits under iteration correspond to solutions of the nonlinear difference equation xn+2 = 1/2(a - b)[xn+1] + 1/2(a + b)xn+1 - xn. This family of piecewise-linear maps has the parameter space (a, b] ϵ R². These maps are area-preserving homeomorphisms of R² that map rays from the origin into rays from the origin. The action on rays gives an auxiliary map Sab: S¹ ↵ S¹ of the circle, which has a well-defined rotation number This paper characterizes the possible dynamics under iteration of Tab when the auxiliary map Sab has rational rotation number, It characterizes cases where the map Tab is a periodic map. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10236198
- Volume :
- 11
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Journal of Difference Equations & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 19090664
- Full Text :
- https://doi.org/10.1080/10236190500273069