On the components of the unstable set of isolated invariant sets

The aim of this note is to shed some light on the topological structure of the unstable set of an isolated invariant set K. We give a bound on the number of essential quasicomponents of the unstable set of K in terms of the homological Conley index of K. The proof relies on an explicit pairing betwe...

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Bibliographic Details
Published in:Topology and its applications 2023-11, Vol.339, p.108581, Article 108581
Main Authors: Hernández-Corbato, Luis, Nieves-Rivera, David Jesús, Ruiz del Portal, Francisco R., Sánchez-Gabites, Jaime J.
Format: Article
Language:English
Subjects:
Alexander-Spanier cohomology
Isolated invariant sets
Quasicomponents
Unstable set
Čech homology
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Summary:The aim of this note is to shed some light on the topological structure of the unstable set of an isolated invariant set K. We give a bound on the number of essential quasicomponents of the unstable set of K in terms of the homological Conley index of K. The proof relies on an explicit pairing between Čech homology classes and Alexander–Spanier cohomology classes that takes the form of an integral.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2023.108581