Abstract
For a dynamical system { S t } on a metric space X, we examine the question whether the topological properties of X are inherited by the global attractor A (if it exists). When { S t } is jointly continuous, we prove that the Čech–Alexander–Spanier cohomology groups of A are isomorphic to the corresponding cohomology groups of X. The same conclusion is obtained in the case where { S t } is a group and A has a bounded neighborhood which is a deformation retract of X.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
