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Morse decompositions and connection matrices

Published online by Cambridge University Press:  10 December 2009

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Abstract

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This paper surveys the work of Charles Conley and his students on Morse decompositions for flows on compact metric spaces, as well as the more recent development of the connection matrix formalism for detecting connections between the Morse sets of a Morse decomposition.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1988

References

REFERENCES

Bowen, R.. On Axiom A Diffeomorphisms. CBMS Regional Conference Series 35. AMS, Providence, RI (1978).Google Scholar
Conley, C.. Isolated Invariant Sets and the Morse Index. CBMS Regional Conference Series 38. AMS, Providence, RI (1978).10.1090/cbms/038Google Scholar
Conley, C.. The gradient structure of a flow: I. Ergod. Th. & Dynam. Sys. 8* (1988), 1126.10.1017/S0143385700009305Google Scholar
Conley, C. & Easton, R.. Isolated invariant sets and isolating blocks. Trans. AMS 158 (1971), 3561.10.1090/S0002-9947-1971-0279830-1Google Scholar
Conley, C. & Zehnder, E.. Morse type index theory for flows and periodic solutions of Hamiltonian systems. Commun. Pure Appl. Math. XXXVII (1984), 207253.Google Scholar
Franks, J.. Homology and Dynamical Systems. CBMS Regional Conference Series 49. AMS, Providence, RI (1982).Google Scholar
Franzosa, R.. Index filtrations and the homology index braid for partially ordered Morse decompositions. Trans. AMS 298 (1986), 193213.10.1090/S0002-9947-1986-0857439-7Google Scholar
Franzosa, R.. The connection matrix theory for Morse decompositions. Preprint. University of Maine (1986).Google Scholar
Kurland, H.. Homotopy invariants of repeller-attractor pairs, I. J. Differential Equations 46 (1982), 131;Google Scholar
J. Differential Equations 49 (1983), 281329.Google Scholar
Milnor, J.. Morse Theory. Annals of Mathematics Studies 51. Princeton University Press, Princeton, NJ.Google Scholar
Mischaikov, K.. Classification of traveling wave solutions of reaction-diffusion equations. Report 86-5. Lefschetz Center for Dynamical Systems (1985).Google Scholar
Morse, M.. The Calculus of Variations in the Large. AMS, New York (1934).Google Scholar
Reineck, J.. The connection matrix and the classification of flows arising from ecological models. Thesis. University of Wisconsin-Madison (1985).Google Scholar
Salamon, D.. Connected simple systems and the Conley index of isolated invariant sets. Trans. AMS 291 (1985), 141.Google Scholar