Stretching of material lines and surfaces in systems with Lagrangian chaos

The problem of the stretching of material lines and surfaces in fluids described by simple Lagrangian equations is revised using methods and tools borrowed from the theory of dynamical systems. The approach allows us to show that some results, previously obtained in the theory of developed turbulence, preserve their validity if one disregards Eulerian behavior and focuses the attention merely on Lagrangian chaoticity. In particular it is possible to show that if the velocity fields have well-defined and almost general symmetry properties, one finds exact coincidence between dynamical evolutions of lines and areas.