Attractors and symmetries of vector fields: The inverse problem

The inverse problem of constructing dynamical systems X with a prescribed compact attracting set K ⊂ Rn and non-trivial dynamics on it is solved. The boundaries ∂ of the attracting basins corresponding to different connected components of K and the relationship between the symmetries of K, X and ∂ are also studied. © 2007 Elsevier Inc. All rights reserved