Lecture 10 - Thu 2020 10 01 - Virtual
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Finish linear phase plane.  \dot{X} = A X;  A = 2x2 matrix.
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Re-draw Delta-tau diagram for eigenvalues lambda = tau/2 + (tau^2/4-Delta)^0.5
Note that going across the dividing lines between saddles, nodes, and spirals
are bifurcations. But some are not stable to nonlinear perturbations.

Attracting and repelling critical points.
Point out "degeneracy" when linear theory fails for \Delta = 0.            ##
Meta-theorem. When is linear picture not structurally stable. Do pictures. ##
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STABILITY JARGON: Lyapunov stable;  Attracting;  AND  Asymptotically
                  stable. Example of attracting but not Lyapunov stable.

Do "EXAMPLES" and beyond in Lecture 9.
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