Moroz, I. M. and Letellier, C. and Gilmore, R. (2007) When are projections also embeddings? Physical Review E, 75 (4).

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Abstract
We study an autonomous fourdimensional dynamical system used to model certain geophysical processes.This system generates a chaotic attractor that is strongly contracting, with four Lyapunov exponents that satisfy , so the Lyapunov dimension is in the range of coupling parameter values studied. As a result, it should be possible to find threedimensional spaces in which the attractors can be embedded so that topological analyses can be carried out to determine which stretching and squeezing mechanisms generate chaotic behavior. We study mappings into to determine which can be used as embeddings to reconstruct the dynamics. We find dramatically different behavior in the two simplest mappings: projections from to . In one case the oneparameter family of attractors studied remains topologically unchanged for all coupling parameter values. In the other case, during an intermediate range of parameter values the projection undergoes selfintersections, while the embedded attractors at the two ends of this range are topologically mirror images of each other.
Item Type:  Article 

Subjects:  D  G > Geophysics D  G > Dynamical systems and ergodic theory O  Z > Ordinary differential equations D  G > General topology 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics 
ID Code:  586 
Deposited By:  Irene Moroz 
Deposited On:  20 Apr 2007 
Last Modified:  29 May 2015 18:24 
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