Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Attractors: persistence, and density of their basins


Author: Mike Hurley
Journal: Trans. Amer. Math. Soc. 269 (1982), 247-271
MSC: Primary 58F12; Secondary 54H20, 58F10
MathSciNet review: 637037
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F12, 54H20, 58F10

Retrieve articles in all journals with MSC: 58F12, 54H20, 58F10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0637037-7
PII: S 0002-9947(1982)0637037-7
Keywords: Attractor, quasi-attractor, chain recurrence, chain transitivity
Article copyright: © Copyright 1982 American Mathematical Society