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SUMMARY:Subcritical instability in shear flows: the shape of the basin bou
 ndary - Lebovitz\, N (Chicago)
DTSTART:20080910T161000Z
DTEND:20080910T163000Z
UID:TALK13369@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The boundary of the basin of attraction of the stable\, lamina
 r point is investigated for several of the dynamical systems modeling subc
 ritical instability. In the cases thus far considered\, this boundary cont
 ains a linearly unstable structure (equilibrium point or periodic orbit). 
 The stable manifold of this unstable structure coincides at least locally 
 with the basin boundary. The unstable structure plays a decisive role in m
 ediating the transition in that transition orbits cluster tightly around i
 ts (one-dimensional) unstable manifold\, illustrating a scenario proposed 
 by Waleffe. The picture that emerges augments the bypass scenario for tran
 sition and reconciles it with Waleffe's scenario. \n\nWe consider a model 
 proposed by Waleffe (W97) for which an unstable equilibrium point U lies o
 n the basin boundary. We find numerically that all orbits starting near U 
 decay to the origin\, whereas 'half' of them should remain permanently bou
 nded away from the origin. We offer an interpretation of this tendency tow
 ard decay based on the structure of the basin boundary.
LOCATION:Seminar Room 1\, Newton Institute
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