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)


Hyperbolic limit sets

Author: Sheldon E. Newhouse
Journal: Trans. Amer. Math. Soc. 167 (1972), 125-150
MSC: Primary 58F15; Secondary 34C35
MathSciNet review: 0295388
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Many known results for diffeomorphisms satisfying Axiom A are shown to be true with weaker assumptions. It is proved that if the negative limit set $ {L^ - }(f)$ of a diffeomorphism f is hyperbolic, then the periodic points of f are dense in $ {L^ - }(f)$. A spectral decomposition theorem and a filtration theorem for such diffeomorphisms are obtained and used to prove that if $ {L^ - }(f)$ is hyperbolic and has no cycles, then f satisfies Axiom A, and hence is $ \Omega $-stable. Examples are given where $ {L^ - }(f)$ is hyperbolic, there are cycles, and f fails to satisfy Axiom A.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F15, 34C35

Retrieve articles in all journals with MSC: 58F15, 34C35

Additional Information

PII: S 0002-9947(1972)0295388-6
Keywords: Limit set, hyperbolic, periodic point, topologically transitive, filtration, basic set, stable manifold, nonwandering
Article copyright: © Copyright 1972 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