Abstract
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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Collet, P. Amplitude Equation for Lattice Maps, A Renormalization Group Approach. Journal of Statistical Physics 90, 1075–1105 (1998). https://doi.org/10.1023/A:1023212925677
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DOI: https://doi.org/10.1023/A:1023212925677