Algebraic transition matrices in the conley index theory

Robert Franzosa, Konstantin Mischaikow

Research output: Contribution to journalArticle

10 Scopus citations


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 examples of how these results can be applied are also presented.

Original languageEnglish (US)
Pages (from-to)889-912
Number of pages24
JournalTransactions of the American Mathematical Society
Issue number3
Publication statusPublished - Dec 1 1998
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


  • Bistable attractor
  • Conley index
  • Connection matrix
  • Transition matrix
  • Travelling waves

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