## Attractors: persistence, and density of their basins

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- by Mike Hurley PDF
- Trans. Amer. Math. Soc.
**269**(1982), 247-271 Request permission

## Abstract:

An investigation of qualitative features of flows on manifolds, in terms of their attractors and quasi-attractors. A quasi-attractor is any nonempty intersection of attractors. It is shown that quasi-attractors other than attractors occur for a large set of flows. It is also shown that for a generic flow (for each flow in a residual subset of the set of all flows), each attractor "persists" as an attractor of all nearby flows. Similar statements are shown to hold with "quasi-attractor", "chain transitive attractor", and "chain transitive quasi-attractor" in place of "attractor". Finally, the set of flows under which almost all points tend asymptotically to a chain transitive quasi-attractor is characterized in terms of stable sets of invariant sets.## References

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## Additional Information

- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**269**(1982), 247-271 - MSC: Primary 58F12; Secondary 54H20, 58F10
- DOI: https://doi.org/10.1090/S0002-9947-1982-0637037-7
- MathSciNet review: 637037