## Topological Methods in Nonlinear Analysis

### Generalized topological transition matrix

#### 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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 48, Number 1 (2016), 183-212.

Dates
First available in Project Euclid: 30 September 2016

https://projecteuclid.org/euclid.tmna/1475266377

Digital Object Identifier
doi:10.12775/TMNA.2016.046

Mathematical Reviews number (MathSciNet)
MR3561428

Zentralblatt MATH identifier
1362.37038

#### Citation

Franzosa, Robert; de Rezende, Ketty A.; Vieira, Ewerton R. Generalized topological transition matrix. Topol. Methods Nonlinear Anal. 48 (2016), no. 1, 183--212. doi:10.12775/TMNA.2016.046. https://projecteuclid.org/euclid.tmna/1475266377

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