Connection matrices and transition matrices

Christopher McCord; James Reineck

Banach Center Publications (1999)

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

Abstract

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

How to cite

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McCord, 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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  1. [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. [2] C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Reg. Conf. Ser. in Math., 38, AMS, Providence, 1978. 
  3. [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. [4] R. Franzosa, Index filtrations and the homology index braid for partially ordered Morse decompositions, Trans. AMS 298 (1986), 193-213. Zbl0626.58013
  5. [5] R. Franzosa, The connection matrix theory for Morse decompositions, Trans. AMS 311 (1989), 781-803. Zbl0708.58021
  6. [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. Zbl0898.34047
  7. [7] C. McCord, The connection map for attractor-repeller pairs, Trans. AMS 308 (1988), 195-203. Zbl0646.34056
  8. [8] C. McCord and K. Mischaikow, Connected simple systems, transition matrices and heteroclinic bifurcations, Trans. AMS 333 (1992), 397-422. Zbl0763.34028
  9. [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. [10] J. Reineck, Connecting orbits in one-parameter families of flows, Erg. Thy. & Dyn. Sys. 8* (1988), 359-374. Zbl0675.58034
  11. [11] J. Reineck, The connection matrix in Morse-Smale flows, Trans. AMS 322 (1990), 523-545. Zbl0714.58027
  12. [12] J. Reineck, A connection matrix analysis of ecological models, Nonlin. Anal. 17 (1991), 361-384. Zbl0739.92022
  13. [13] Connection matrix pairs for the discrete Conley index, preprint. Available at http:/www.math.nwu.edu/~richeson. 
  14. [14] D. Salamon, Connected Simple Systems and the Conley index of isolated invariant sets, Trans. AMS 291 (1985), 1-41. Zbl0573.58020
  15. [15] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, 1980. Zbl0508.35002
  16. [16] E. Spanier, Algebraic Topology, McGraw Hill, 1966, Springer-Verlag, New York, 1982. 

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