SCENARIO FOR THE ONSET OF SPACE-TIME CHAOS

The onset of space-time chaos is studied on the basis of a Galilean in variant model that exhibits the essential characteristics of the pheno menon. By keeping the linear part of the model extremely simple, one h as better than usual control of the classes of available stationary so lutions. These stationary solutions include not only spatially periodi c but also a large set of spatially chaotic solutions that can be char acterized by words of a symbolic language. The main proposition of thi s paper is that space-time chaos in Galilean invariant models can be u nderstood in a qualitative fashion as an orbit in the space of functio ns that visits words in this language in a random fashion. The appeara nce of topological defects and other ''signatures'' of space-time chao s are a natural consequence of this dynamics. Finally, we construct a simple demonstration of this scenario.