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- Title
ON PLANAR PIECEWISE AND TWO-TORUS PARABOLIC MAPS.
- Authors
Ashwin, Peter; Xinchu Fu; Lin, Congping
- Abstract
We investigate properties and examples of iterated planar piecewise parabolic (PWP) maps, including those induced by two-torus parabolic maps and their inverses. PWP maps are area-preserving maps that have constant linearizations but only one eigenvector with eigenvalue one. We obtain necessary and sufficient conditions for a two-torus parabolic map to be invertible. For noninvertible PWP maps, there are a number of questions about the existence and structure of attractors for such maps. We introduce the simplest example of a nontrivial PWP map, defined by a parabolic linear map with a translation that is a different constant on each side of a given line in the plane. For this "half plane parabolic map" we obtain sufficient conditions for a bounded attractor to exist, discuss their dynamical properties and give some examples of these and related maps.
- Subjects
EIGENVALUES; PIECEWISE linear topology; PARABOLIC operators; BIFURCATION theory; ATTRACTORS (Mathematics); LINEAR operators
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2009, Vol 19, Issue 7, p2383
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127409024153