On the two definitions of the Conley index

Kurland, Henry L.

doi:10.1090/S0002-9939-1989-0982405-9

On the two definitions of the Conley index
HTML articles powered by AMS MathViewer

by Henry L. Kurland PDF

Proc. Amer. Math. Soc. 106 (1989), 1117-1130 Request permission

Abstract:

The two definitions of the homotopy equivalences between Conley index spaces of an isolated invariant set, the original one of Conley [C] as completed by the author in [K1] and the more recent definition of Salamon [S], are shown to define the same homotopy classes without reference to the difficult proof of [K1] showing the Conley index to be a connected simple system. The equivalences of the original definition are useful in describing certain geometric situations in terms of the index; examples are given.

References

The two-point problem for a class of ordinary differential equations with a small parameter coefficient of the derivative

10

Charles Conley, Isolated invariant sets and the Morse index, CBMS Regional Conference Series in Mathematics, vol. 38, American Mathematical Society, Providence, R.I., 1978. MR 511133
Henry L. Kurland, The Morse index of an isolated invariant set is a connected simple system, J. Differential Equations 42 (1981), no. 2, 234–259. MR 641650, DOI 10.1016/0022-0396(81)90028-0
Henry L. Kurland, Homotopy invariants of repeller-attractor pairs. I. The Puppe sequence of an R-A pair, J. Differential Equations 46 (1982), no. 1, 1–31. MR 677580, DOI 10.1016/0022-0396(82)90106-1
Henry L. Kurland, Homotopy invariants of repeller-attractor pairs. II. Continuation of R-A pairs, J. Differential Equations 49 (1983), no. 2, 281–329. MR 708647, DOI 10.1016/0022-0396(83)90016-5
Henry L. Kurland, Following homology in singularly perturbed systems, J. Differential Equations 62 (1986), no. 1, 1–72. MR 830047, DOI 10.1016/0022-0396(86)90105-1

Layers in singularly perturbed systems via homology contintuation

Dietmar Salamon, Connected simple systems and the Conley index of isolated invariant sets, Trans. Amer. Math. Soc. 291 (1985), no. 1, 1–41. MR 797044, DOI 10.1090/S0002-9947-1985-0797044-3