Connection matrices and transition matrices

• Autorzy: Christopher McCord , James F. Reineck
• Języki publikacji: EN

Abstrakty

EN

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1999
• Tom: 47
• Numer: 1
• Strony: 41-55

Daty

wydano

1999

Twórcy

autor

Christopher McCord

• Department of Mathematics, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221-0025, U.S.A.

autor

James F. Reineck

• Department of Mathematics, SUNY at Buffalo, Buffalo, New York 14214, U.S.A.

Bibliografia

• [1] L. Arnold, C. Jones, K. Mischaikow and G. Raugel, Dynamical Systems Montecatini Terme 1994, R. Johnson, ed., Lect. Notes Math. 1609, Springer, 1995.
• [2] C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Reg. Conf. Ser. in Math., 38, AMS, Providence, 1978.
• [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.
• [4] R. Franzosa, Index filtrations and the homology index braid for partially ordered Morse decompositions, Trans. AMS 298 (1986), 193-213.
• [5] R. Franzosa, The connection matrix theory for Morse decompositions, Trans. AMS 311 (1989), 781-803.
• [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.
• [7] C. McCord, The connection map for attractor-repeller pairs, Trans. AMS 308 (1988), 195-203.
• [8] C. McCord and K. Mischaikow, Connected simple systems, transition matrices and heteroclinic bifurcations, Trans. AMS 333 (1992), 397-422.
• [9] C. McCord and K. Mischaikow, Equivalence of topological and singular transition matrices in the Conley index, Mich. Math. J. 42 (1995), 387-414.
• [10] J. Reineck, Connecting orbits in one-parameter families of flows, Erg. Thy. & Dyn. Sys. 8* (1988), 359-374.
• [11] J. Reineck, The connection matrix in Morse-Smale flows, Trans. AMS 322 (1990), 523-545.
• [12] J. Reineck, A connection matrix analysis of ecological models, Nonlin. Anal. 17 (1991), 361-384.
• [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.
• [15] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, 1980.
• [16] E. Spanier, Algebraic Topology, McGraw Hill, 1966, Springer-Verlag, New York, 1982.