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— We study space-penodic damped and driven cubic Schrodinger équations in one dimension. In a previous work, we have shown that the long time behavior of these équations was governed by a finite-dimensional attractor. Here our aim is to provide upper and lower bounds on this dimension which are exphcit in terms of the data.

Explicit upper and lower bounds on the number of degrees of freedom for damped and driven cubic Schrödinger equations