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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Transition matrix theory


Authors: Robert Franzosa and Ewerton R. Vieira
Journal: Trans. Amer. Math. Soc. 369 (2017), 7737-7764
MSC (2010): Primary 37B30, 37D15; Secondary 70K70, 70K50, 55T05
DOI: https://doi.org/10.1090/tran/6915
Published electronically: August 15, 2017
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Abstract:

In this article we present a unification of the theory of algebraic, singular, topological and directional transition matrices by introducing the (generalized) transition matrix which encompasses each of the previous four. Some transition matrix existence results are presented as well as verification that each of the previous transition matrices are cases of the (generalized) transition matrix. Furthermore we address how applications of the previous transition matrices to the Conley index theory carry over to the (generalized) transition matrix.


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Additional Information

Robert Franzosa
Affiliation: Departament of Mathematics and Statistics, University of Maine, Orono, Maine 04469
Email: robert$_$franzosa@umit.maine.edu

Ewerton R. Vieira
Affiliation: Instituto de Matemática e Estátistica, Universidade Federal de Goiás, Goiânia, Goiás, Brazil
Email: ewerton@ufg.br

DOI: https://doi.org/10.1090/tran/6915
Received by editor(s): February 26, 2015
Received by editor(s) in revised form: November 11, 2015
Published electronically: August 15, 2017
Additional Notes: The second author was partially supported by FAPEG under grant 2012/10 26 7000 803 and FAPESP under grant 2010/19230-8
Dedicated: Dedicated to the memory of James Francis Reineck
Article copyright: © Copyright 2017 American Mathematical Society

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