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Explicit invariant manifolds and specialised trajectories in a class of unsteady flows
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10.1063/1.4769979
/content/aip/journal/pof2/24/12/10.1063/1.4769979
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/12/10.1063/1.4769979
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The flow of the steady version of Duffing's equation (16), with the “bow-tie” manifold structure shown as the thick curve.

Image of FIG. 2.
FIG. 2.

Five snapshots in time of the manifolds associated with (20) the Duffing equation with transformation (19).

Image of FIG. 3.
FIG. 3.

Evolution of the first elliptic trajectory (solid curve) associated with the transformation (24), and several nearby trajectories (dashed curves).

Image of FIG. 4.
FIG. 4.

Several time slices of the heteroclinic manifold structure of the Duffing equation subject to the transformation (24).

Image of FIG. 5.
FIG. 5.

A schematic of the stagnation points and their invariant manifolds in the steady Hill's spherical vortex.

Image of FIG. 6.
FIG. 6.

The evolution of the ring of elliptic points in Hill's spherical vortex transformed using (32), that is, for the flow given by (C3)+(C4), for the parameter choice U = 1, c = 1, μ = −1/2, and ω = 2π.

Image of FIG. 7.
FIG. 7.

The heteroclinic manifold for Hill's spherical vortex transformed using (32), that is, for the flow given by (C3)+(C4), for the parameter choice U = 1, c = 1, μ = −1/2, and ω = 2π. The four panels show (a) t = −1, (b) t = −0.5, (c) t = 0, and (d) t = 0.5.

Image of FIG. 8.
FIG. 8.

The flow of the steady version of the nonhyperbolic Duffing equation (46), with deformed bow-tie manifold structure shown as the thick curve.

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/content/aip/journal/pof2/24/12/10.1063/1.4769979
2012-12-11
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Explicit invariant manifolds and specialised trajectories in a class of unsteady flows
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/12/10.1063/1.4769979
10.1063/1.4769979
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