Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The connection map for attractor-repeller pairs


Author: Christopher McCord
Journal: Trans. Amer. Math. Soc. 307 (1988), 195-203
MSC: Primary 58F12; Secondary 34C35
MathSciNet review: 936812
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the Conley index theory, the connection map of the homology attractor-repeller sequence provides a means of detecting connecting orbits between a repeller and attractor in an isolated invariant set. In this work, the connection map is shown to be additive: under suitable decompositions of the connecting orbit set, the connection map of the invariant set equals the sum of the connection maps of the decomposition elements. This refines the information provided by the homology attractor-repeller sequence. In particular, the properties of the connection map lead to a characterization of isolated invariant sets with hyperbolic critical points as an attractor-repeller pair.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F12, 34C35

Retrieve articles in all journals with MSC: 58F12, 34C35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0936812-4
PII: S 0002-9947(1988)0936812-4
Keywords: Conley index, attractor-repeller pair, connection map
Article copyright: © Copyright 1988 American Mathematical Society