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1999 | 47 | 1 | 41-55
Tytuł artykułu

Connection matrices and transition matrices

Treść / Zawartość
Warianty tytułu
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.
Słowa kluczowe
Rocznik
Tom
47
Numer
1
Strony
41-55
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Department of Mathematics, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221-0025, U.S.A.
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv47i1p41bwm
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