Matrizes de conexão via o complexo de Morse-Witten

TL;DRAbstract

Given a smooth closed manifold M , the Morse-Witten complex associated to a Morse function f : M R and a Riemannian metric g on M consists of chain groups generated by the critical points of f and a boundary operator counting isolated flow lines of the negative gradient flow. The homology of the Morse-Witten complex is isomorphic to the singular homology of M. Give a isolated invariant set S, a connection matrix for a Morse decomposition of S is a matrix of homomorphism between the Conley homology indices of Morse sets. The connection matrix is capable of providing dynamical information of a flow. In fact, this matrix can detect the existence of connecting orbits among Morse sets of S.

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