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Given a one-parameter family of flows over a parameter interval Λ, assuming there is a continuation of Morse decompositions over Λ, Reineck (1988) defined a singular transition matrix to show the existence of a connecting orbit between some Morse sets at some parameter points in Λ. This talk aims to extend the definition of a singular transition matrix in cases where there is no continuation of Morse decompositions over the parameter interval. This extension will help study the bifurcation associated with the change of Morse decomposition from a topological dynamics viewpoint.

余楊鴻，京都大學碩士研究生，現為東京工業大學博士。主要研究方向是動力系統的分岔理論，Conley index和轉移矩陣。