Fractal basin boundaries generated by basin cells and the geometry of mixing chaotic flows
Experiments and computations indicate that mixing in chaotic flows generates certain coherent spatial structures. If a two-dimensional basin has a basin cell (a trapping 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 for 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.
Nusse
HE
Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
Yorke
JA