Topological properties of attractors for dynamical systems

  • Gobbino M
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Abstract

For a dynamical system {St} 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 {St} 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 {St} is a group and A has a bounded neighborhood which is a deformation retract of X. © 1999 Elsevier Science B.V.

Author-supplied keywords

  • 34D45
  • 55N05
  • Direct and inverse limit
  • Dynamical system
  • Global attractor
  • Semigroup
  • Čech-Alexander-Spanier cohomology

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Authors

  • Massimo Gobbino

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