It is known that any isolated invariant set can be decompose into two isolated invariant sets (the attractor and the dual repeller) and the connecting orbits between them. Detection of these connecting orbits is a central problem in the qualitative analysis of differential equations. The Conley index theory provides a tool to partially solve this problem by attaching to an isolated invariant set a pointed topological space (the index) and then construct a long exact sequence in terms of homologies/cohomologies of the invariant set and the attractor and the repeller that decompose it. The...
It is known that any isolated invariant set can be decompose into two isolated invariant sets (the attractor and the dual repeller) and the connecting...