This paper is an introduction to connection and transition matrices in the Conley index theory for flows. Basic definitions and simple examples are discussed.
@article{bwmeta1.element.bwnjournal-article-bcpv47i1p41bwm,
author = {McCord, Christopher and Reineck, James},
title = {Connection matrices and transition matrices},
journal = {Banach Center Publications},
volume = {50},
year = {1999},
pages = {41-55},
zbl = {0946.37005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv47i1p41bwm}
}
McCord, Christopher; Reineck, James. Connection matrices and transition matrices. Banach Center Publications, Tome 50 (1999) pp. 41-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv47i1p41bwm/
[000] [1] L. Arnold, C. Jones, K. Mischaikow and G. Raugel, Dynamical Systems Montecatini Terme 1994, R. Johnson, ed., Lect. Notes Math. 1609, Springer, 1995.
[001] [2] C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Reg. Conf. Ser. in Math., 38, AMS, Providence, 1978.
[002] [3] C. Conley, A qualitative singular perturbation theorem, Global Theory of Dynamical Systems, (eds. Z. Nitecki and C. Robinson), Lecture Notes in Math. 819, Springer-Verlag 1980, 65-89.
[003] [4] R. Franzosa, Index filtrations and the homology index braid for partially ordered Morse decompositions, Trans. AMS 298 (1986), 193-213. | Zbl 0626.58013
[004] [5] R. Franzosa, The connection matrix theory for Morse decompositions, Trans. AMS 311 (1989), 781-803. | Zbl 0708.58021
[005] [6] H. Kokubu, K. Mischaikow and H. Oka, Existence of infinitely many connecting orbits in a singularly perturbed ordinary differential equation, Nonlinearity 9 (1996), 1263-1280. | Zbl 0898.34047
[006] [7] C. McCord, The connection map for attractor-repeller pairs, Trans. AMS 308 (1988), 195-203. | Zbl 0646.34056
[007] [8] C. McCord and K. Mischaikow, Connected simple systems, transition matrices and heteroclinic bifurcations, Trans. AMS 333 (1992), 397-422. | Zbl 0763.34028
[008] [9] C. McCord and K. Mischaikow, Equivalence of topological and singular transition matrices in the Conley index, Mich. Math. J. 42 (1995), 387-414. | Zbl 0853.58080
[009] [10] J. Reineck, Connecting orbits in one-parameter families of flows, Erg. Thy. & Dyn. Sys. 8* (1988), 359-374. | Zbl 0675.58034
[010] [11] J. Reineck, The connection matrix in Morse-Smale flows, Trans. AMS 322 (1990), 523-545. | Zbl 0714.58027
[011] [12] J. Reineck, A connection matrix analysis of ecological models, Nonlin. Anal. 17 (1991), 361-384. | Zbl 0739.92022
[012] [13] Connection matrix pairs for the discrete Conley index, preprint. Available at http:/www.math.nwu.edu/~richeson.
[013] [14] D. Salamon, Connected Simple Systems and the Conley index of isolated invariant sets, Trans. AMS 291 (1985), 1-41. | Zbl 0573.58020
[014] [15] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, 1980. | Zbl 0508.35002
[015] [16] E. Spanier, Algebraic Topology, McGraw Hill, 1966, Springer-Verlag, New York, 1982.