Short-wavelength instability and transition to chaos in distributed systems with additional symmetry

A review is presented of the theory of pattern forma- tion in extended, dissipative, highly nonequilibrium systems. Emphasis is placed on systems which, in addition to spatial translations and rotations, have additional continuous symme- try group(s). It is shown that the additional symmetry destabi- lizes dramatically the ground state of the system thus causing it to make a direct transition from a spatially uniform to a turbu- lent state in an analogous fashion to the second-order phase transition in quasi-equilibrium systems. Apart from the theore- tical analysis, a discussion of experimental data is given. To the respectful memory of I M Lifshitz.