Simplical models for the global dynamics of attractors (Q1590088)

The author considers a flow \(\phi\) on a compact metric space \(\mathcal{A}\) which has a Morse decomposition \(\{S_p\}_{p\in P}\) indexed by the partially ordered set \((P,<)\). Using Conley index type information on \(\phi\) he constructs a simplicial space \({\mathcal{M}}={\mathcal{M}}(P,<)\), a flow \(\theta\) on \(\mathcal{M}\) and a continuous surjective map \(f:\mathcal{A}\rightarrow\mathcal{M}\) which commutes with the flows up to a reparametrization. The model space \(\mathcal{M}\) has an \(n\)-simplex \([p_0p_1\ldots p_n]\) for each ordered tupel \(p_0<p_1<\ldots<p_n\) in \(P\). Each Morse set \(S_p\) is mapped by \(f\) to the vertex \([p]\).