Generalized Topological Transition Matrix
Dynamical Systems
2013-11-15 v1
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.
Cite
@article{arxiv.1311.3520,
title = {Generalized Topological Transition Matrix},
author = {Robert Franzosa and Ketty A. de Rezende and Ewerton R. Vieira},
journal= {arXiv preprint arXiv:1311.3520},
year = {2013}
}