WIAS Preprint No. 311, (1997)

Strange attractors with topologically simple basins


Authors

  • Bothe, Hans Günter

2010 Mathematics Subject Classification

  • 58F12

Keywords

  • 1-dimensional hyperbolic attractors, attractor basis

DOI

10.20347/WIAS.PREPRINT.311

Abstract

We consider the basin WsΛ of a 1-dimensional hyperbolic attractor Λ in an m-dimensional manifold M where m ≥ 4, WsΛ is orientable and Λ is transversely tame.

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.

Appeared in

  • Topology Appl. 114 (2001) no. 1, pp. 1--25.

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