Q: Harmonic oscillator differential equation dynamical system Is $x''(t) = -ax$ (a simple harmonic oscillator) considered a one-dimensional dynamical system or two-dimensional?
If it is one dimensional, why is this possible? With a dynamical system, isnt it impossible for a one dimensional system to oscillate?
Thank you!

A: It is a second order scalar equation. Its phase or state space has dimension two. The cited claim on non-oscillation is only true for scalar first-order autonomous equations.
