Generalized topological transition matrix

Robert Franzosa, Ketty A. de Rezende, Ewerton R. Vieira

DOI: http://dx.doi.org/10.12775/TMNA.2016.046

Abstract


This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this more general transition matrix satisfies the additional requirement that it covers flow-defined Conley-index isomorphisms, one proves algebraic and connection-existence properties. These general transition matrices with this covering property are referred to as generalized topological transition matrices and are used to consider connecting orbits of Morse-Smale flows without periodic orbits, as well as those in a continuation associated to a dynamical spectral sequence.

Keywords


Conley index; connection matrices; transition matrices; Morse-Smale system; sweeping method; spectral sequence

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References


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