Amplitude Equation for Lattice Maps, a Renormalization Group Approach
arXiv:patt-sol/9705011 · doi:10.1023/A:1023212925677
Abstract
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.
25 pages, plain TeX