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.

Topological properties of attractors for dynamical systems

GOBBINO, MASSIMO
2001-01-01

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.
2001
Gobbino, Massimo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/187155
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