ENTROPY BY UNIT LENGTH FOR THE GINZBURG-LANDAU EQUATION ON THE LINE. A HILBERT SPACE FRAMEWORK.

It is well-known that the Ginzburg-Landau equation on R has a global attractor [15] that attracts in Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. (ℝ) all the trajectories. This attractor contains bounded trajectories that are analytical functions in space. A famous theorem due to P. Collet and JP. Eckmann asserts that the ε-entropy per unit length in L∞ of this global attractor is finite and is smaller than the corresponding complexity for the space of functions which are analytical in a strip. This means that the global attractor is flatter than expected. We explain in this article how to establish the Collet-Eckmann Theorem in a Hilbert space framework. [ABSTRACT FROM AUTHOR]