Scenario for the onset of space-time chaos

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Abstract
The onset of space-time chaos is studied on the basis of a Galilean invariant model that exhibits the essential characteristics of the phenomenon. By keeping the linear part of the model extremely simple, one has better than usual control of the classes of available stationary solutions. These stationary solutions include not only spatially periodic but also a large set of spatially chaotic solutions that can be characterized by words of a symbolic language. The main proposition of this paper is that space-time chaos in Galilean invariant models can be understood in a qualitative fashion as an orbit in the space of functions that visits words in this language in a random fashion. The appearance of topological defects and other “signatures” of space-time chaos are a natural consequence of this dynamics. Finally, we construct a simple demonstration of this scenario.