Characteristic features of the dynamics of the Ginzburg-Landau equation in a plane domain

We study the boundary value problem w_t=ℵ₀Δw+ℵ₁w-ℵ₂w|w|²,w|∂Ω₀=0 in the domain Ω₀={(x,y):0 ≤ x ≤ l₁,0 ≤ y ≤ l₂}. Here, w is a complex-valued function, Δ is the laplace operator, and ℵ_j, j=0,1,2, are complex constants withRe ℵ_j > 0. We show that under a rather general choice of the parameters l₁ and l₂, the number of stable invariant tori in the problem, as well as their dimensions, grows infinitely asRe ℵ₀ → 0 andRe ℵ₀ → 0. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 2, pp. 205–220, November, 2000.