Fractal basin boundaries generated by basin cells and the geometry of mixing chaotic flows

Experiments and computations indicate that mixing in chaotic flows generate s certain coherent spatial structures. Lf a two-dimensional basin has a bas in cell (a trappings region whose boundary consists of pieces of the stable and unstable manifold of some periodic orbit) then the basin consists of a central body (the basin cell) and a finite number of channels: attached to it and the basin boundary is fractal. We demonstrate an amazing property f or certain global structures: A basin has a basin cell if and only if every diverging curve comes close to every basin boundary point of that basin.