Amplitude Equation for Lattice Maps, a Renormalization Group Approach

Details Amplitude Equation for Lattice Maps, a Renormalization Group Approach Amplitude Equation for Lattice Maps, a Renormalization Group Approach

1997-05-22

arxiv.org/abs/patt-sol/9705011v1

Nonlinear Sciences

Pattern Formation and Solitons

25 pages, plain TeX

Scientific paper

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.

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