Equivalence of topological and singular transition matrices in the Conley index theory
Consider a continuous flow on a locally compact Hausdorff space and the maximal invariant set \(S\). A Morse decomposition is a collection of mutually disjoint invariant subsets of \(S\) indexed by some finite set. A difficult problem is to understand the flow in all \(S\) from the Morse decomposition. Conley index and Conley connection matrix are introduced to deal with questions related to this problem. Morse decompositions and connection matrices provide a framework in which one can detect global bifurcation. Transition matrices, which allow for interpreting the implications of differences in connection matrices, can be constructed in three different ways: singular, topological and algebraic. The purpose of this paper is to relate singular and topological transition matrices, showing that they are equivalent.
scientific article; zbMATH DE number 838738