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

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Generic homeomorphisms have no smallest attractors

Author: Mike Hurley
Journal: Proc. Amer. Math. Soc. 123 (1995), 1277-1280
MSC: Primary 58F12
MathSciNet review: 1273500
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that if M is a compact manifold then there is a residual subset $ \mathcal{R}$ of the set of homeomorphisms on M with the property that if $ f \in \mathcal{R}$ then f has no smallest attractor (that is, an attractor with the property that none of its proper subsets is also an attractor). Part of the motivation for this result comes from portions of a recent paper by Lewowicz and Tolosa that deal with properties of smallest attractors of generic homeomorphisms.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F12

Retrieve articles in all journals with MSC: 58F12

Additional Information

PII: S 0002-9939(1995)1273500-0
Keywords: Attractor, generic homeomorphism
Article copyright: © Copyright 1995 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia