Ordinary Differential Equations and Dynamical Systems Vol2 · Problem 6.2

Linearization and Invariant Manifolds

Mathematics — Calculus · fundamental-matrix-smooth-dependence-parameters

Problem

Show that the fundamental matrix

X(t; \omega, \varepsilon)

of the Mathieu equation

x'(t) = \begin{bmatrix} 0 & 1 \\ -(\omega^2 + \varepsilon \cos t) & 0 \end{bmatrix} x(t)

belongs to

C^\infty(\mathbb{R}^3)