Spatio-Temporal Chaos

Continuous physical systems, such as electromagnetic fields or fluids, are described dynamically by partial differential equations, or field theories. Thus they have infinitely many degrees of freedom; accordingly, it came as a surprise at the end of the seventies that such systems can exhibit low dimensional chaos which is characteristic of systems with few degrees of freedom. In the meanwhile this miracle has been fully understood. By keeping a fluid in a box which is not too large compared to some typical macroscopic scale (like the size of a convection roll) one can maintain spatial coherence but the system will become temporally chaotic. Only a few spatial modes get appreciably excited, and their amplitudes define a low-dimensional “phase-space” in which the chaotic dynamics takes place