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Amplitude Equation for Lattice Maps, a Renormalization Group Approach

We consider the development of instabilities of homogeneous stationary solutions of discrete time lattice maps. Under some generic hypothesis we derive an amplitude equation which is the space-time continuous Ginzburg-Landau equation. Using dynamical renormalization group methods we control the accuracy of this approximation in a large ball of its basin of attraction.

preprint1997arXivOpen access
P. Collet
patt-solnlin.PS
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