Aha moment

by Brenda McCaffrey

If stable and unstable manifolds are nonlinear analogs to eigenvectors, then Lyapunov exponents are analogous to eigenvalues in nonlinear systems.  Bends and folds in the terrain are the source of the dependence on initial conditions, and the structure of chaotic attractors.

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YES! :) Except that I’d say the exponents correspond to eigenvalues, whereas the eigenvectors correspond to the tangent spaces to the “expanding” and “contracting” submanifolds normal to the orbits of the dynamical system. Xin Wei
— Xin Wei Sha
YES! :) Except that I’d say the exponents correspond to eigenvalues, whereas the eigenvectors correspond to the tangent spaces to the “expanding” and “contracting” submanifolds normal to the orbits of the dynamical system.
— Sha Xin Wei
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