# Connection matrices and transition matrices

Christopher McCord; James Reineck

Banach Center Publications (1999)

- Volume: 47, Issue: 1, page 41-55
- ISSN: 0137-6934

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topMcCord, Christopher, and Reineck, James. "Connection matrices and transition matrices." Banach Center Publications 47.1 (1999): 41-55. <http://eudml.org/doc/208941>.

@article{McCord1999,

abstract = {This paper is an introduction to connection and transition matrices in the Conley index theory for flows. Basic definitions and simple examples are discussed.},

author = {McCord, Christopher, Reineck, James},

journal = {Banach Center Publications},

keywords = {Conley index; Morse decomposition; connection matrix; transition matrix},

language = {eng},

number = {1},

pages = {41-55},

title = {Connection matrices and transition matrices},

url = {http://eudml.org/doc/208941},

volume = {47},

year = {1999},

}

TY - JOUR

AU - McCord, Christopher

AU - Reineck, James

TI - Connection matrices and transition matrices

JO - Banach Center Publications

PY - 1999

VL - 47

IS - 1

SP - 41

EP - 55

AB - This paper is an introduction to connection and transition matrices in the Conley index theory for flows. Basic definitions and simple examples are discussed.

LA - eng

KW - Conley index; Morse decomposition; connection matrix; transition matrix

UR - http://eudml.org/doc/208941

ER -

## References

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- [4] R. Franzosa, Index filtrations and the homology index braid for partially ordered Morse decompositions, Trans. AMS 298 (1986), 193-213. Zbl0626.58013
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- [8] C. McCord and K. Mischaikow, Connected simple systems, transition matrices and heteroclinic bifurcations, Trans. AMS 333 (1992), 397-422. Zbl0763.34028
- [9] C. McCord and K. Mischaikow, Equivalence of topological and singular transition matrices in the Conley index, Mich. Math. J. 42 (1995), 387-414. Zbl0853.58080
- [10] J. Reineck, Connecting orbits in one-parameter families of flows, Erg. Thy. & Dyn. Sys. 8* (1988), 359-374. Zbl0675.58034
- [11] J. Reineck, The connection matrix in Morse-Smale flows, Trans. AMS 322 (1990), 523-545. Zbl0714.58027
- [12] J. Reineck, A connection matrix analysis of ecological models, Nonlin. Anal. 17 (1991), 361-384. Zbl0739.92022
- [13] Connection matrix pairs for the discrete Conley index, preprint. Available at http:/www.math.nwu.edu/~richeson.
- [14] D. Salamon, Connected Simple Systems and the Conley index of isolated invariant sets, Trans. AMS 291 (1985), 1-41. Zbl0573.58020
- [15] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, 1980. Zbl0508.35002
- [16] E. Spanier, Algebraic Topology, McGraw Hill, 1966, Springer-Verlag, New York, 1982.

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