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September 8, 2026 00:44
- Add based on Michael J. Ward's Basic Floquet Theory - Define , , , - Prove Ward Theorem 3.3(i) and stroboscopic - Prove Ward Theorem 3.4(i) , , and stroboscopic map - Prove Ward Theorem 3.4(ii) x(t) = exp(μ t) • p(t) - Prove Ward §3.1.2 Goldstone multiplier 1 theorem for autonomous periodic orbits - Prove Ward §3.2.3 second-order trace stability criteria - Prove stroboscopic distance contraction and geometric decay
…s to Floquet - Add : Lyapunov stability of origin under stroboscopic flow via - Add : asymptotic trajectory convergence to 0 when ‖M‖ < 1 - Add : attractiveness of origin via - Add : mode convergence to 0 along contracting multiplier |ρ| < 1 - Add : complex roots with ‖z‖ = 1 when |φ| < 1 (Ward §3.2.3 Case I) - Add : unstable real multiplier ρ > 1 when φ > 1 (Ward §3.2.3 Case II)
… power boundedness
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This PR formalizes the core results of Floquet theory for linear differential equations with periodic coefficients, following Michael J. Ward, Basic Floquet Theory, Chapter 3.
Main Contributions
X(t₀, t)satisfyingX(t₀, t₀) = id,X(t₁, t₂) ∘ X(t₀, t₁) = X(t₀, t₂), andd/dt X = L(t) ∘ X.HasShiftInvariance X T(X(t₀ + T, t + T) = X(t₀, t)), proving the Floquet factorization into a periodic component and stroboscopic powers.monodromyandisFloquetMultiplier.Note: Built on top of #67.