Dynamics on the global attractor of a gradient flow arising from the Ginzburg-Landau equation (Q1335562)

The dynamics of the attractor for the complex Ginzburg-Landau equation \[ u_ t = v(1 + ik) u_{xx} + u - (1 + i \mu)| u|^ 2 u \] for \(\mu \approx k\) is described via a semiconjugacy onto a simple ordinary differential equation defined on the unit disk in \(\mathbb{R}^{2k}\).