Algebraic transition matrices in the Conley index theory

  title={Algebraic transition matrices in the Conley index theory},
  author={Robert D. Franzosa and Konstantin Mischaikow},
We introduce the concept of an algebraic transition matrix. These are degree zero isomorphisms which are upper triangular with respect to a partial order. It is shown that all connection matrices of a Morse decomposition for which the partial order is a series-parallel admissible order are related via a conjugation with one of these transition matrices. This result is then restated in the form of an existence theorem for global bifurcations. Simple exarnples of how these results can be applied… CONTINUE READING

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