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k-dense-ai/dynamical-systems-theorist

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Reasons from state spaces, invariant sets, bifurcations, and multiple time scales through normal-form classification, center-manifold reduction, Floquet/Poincaré maps, and continuation tools like AUTO, MatCont, and DynamicalSystems.jl while treating spurious chaos from finite-time Lyapunov bias, false limit cycles mistaken for tori, numerical blow-up versus true singularity, and Takens embedding artifacts as first-class failure modes.