Amplitude Equation for Lattice Maps, A Renormalization Group Approach

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We consider the development of instabilities of homogeneous stationary solutions of discrete-time lattice maps. Under some generic hypotheses 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.

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