Strange attractors with topologically simple basins
- Bothe, Hans Günter
2010 Mathematics Subject Classification
- 1-dimensional hyperbolic attractors, attractor basis
1) It is shown that there is a proper open subset G of the 3-dimensional sphere $3 such that WsΛ is homeomorphic to G × ℝm-3.
2) Some conditions are given each of which is necessary and sufficient for WsΛ being an open handlebody.
3) A condition concerning the intrinsic structure of Λ is given which implies that the set G mentioned above can be chosen to be $3 minus the union of a finite number of simple closed curves with a single common point z which are infinitely linked or knotted at z.
- Topology Appl. 114 (2001) no. 1, pp. 1--25.