References

[Ab-R] R. Abraham and J. Robbin, Transversal Mappings and Flows, W.A. Ben-

jamin, Inc., New York, 1967.

[AnMP] S. Angenent and J. Mallet-Paret, Stable transition layers in a semilinear boundary value problem, J. Differential Equations 67 (1987), 212–242.

[A] V.I. Arnold, Ordinary Differential Equations; translated from the Russian by R.A. Silverman, The MIT Press, Boston, 1978.

[Bg] Yu. P. Boglaev, The two-point problem for a class of ordinary differential equations with a small parameter coefficient of the derivative, USSR Comput. Math.-Math. Phys. 10 (1970), 190–204.

[Ch] R.C. Churchill, Isolated invariant sets in compact metric spaces, J. Differential Equations 12 (1972), 330–352.

[C] C.C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Conference Proceedings, Amer. Math. Soc., Providence, R.I., 1978.

[C-E] C. Conley and R. Easton, Isolated invariant sets and isolating blocks,

Trans. AMS 158 (1971), 35–61.

[D] A. Dold, Lectures on Algebraic Topology, Springer-Verlag, New York, 1972.

[F] R.A. Fisher, The wave of advance of advantageous genes, Ann. of Eugenics 7 (1937), 355–369.

[Ha] J.B.S. Haldane, The theory of a cline, J. Genetics 48 (1948), 277–284.

[H] M.W. Hirsch, Differental Topology, Springer-Verlag, New York, 1976.

[HPS] M.W. Hirsch, C.C. Pugh, and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, vol. 583, Springer-Verlag, New York, 1977.

[H-S] M.W. Hirsch and S. Smale, Differential Equations, Dynamical Systems,

and Linear Algebra, Academic Press, New York, 1974.

[Hus] D. Husemoller, Fibre Bundles, second edition, Springer-Verlag, New York, 1975.

[K1] H.L. Kurland, The Morse index of an isolated invariant set is a connected simple system, J. Differential Equations 42 (1981), 234–259.

[K2] , Homotopy invariants of a repeller-attractor pair, I: the Püppe sequence of an R-A pair, J. Differential Equations 46 (1982), 1–31.

[K3] , Homotopy invariants of a repeller-attractor pair,II: continuation of an R-A pair, J. Differential Equations 49 (1983), 281–329.

[K4] , Following homology in singularly perturbed systems, J. Differential Equations 62 (1986), 1–72.

[K5] , On the two definitions of the Conley index, Proceedings of the AMS 106 (1989), 1117–1130.

[K6] , Monotone and oscillatory solutions of a problem arising in population genetics, Nonlinear Partial Differential Equations (J.A. Smoller, ed.), Contemporary Mathematics, vol. 17, AMS, Providence, R.I., 1983, pp. 323–342.

[K7] , Layers in singularly perturbed systems via homology contintuation, (unpublished typescript).

[Mc1] C.K. McCord, Mappings and homological properties in the Conley index theory, Ergod. Th. & Dynam. Sys. 8∗ (1988), 175–198.

[Mc2] C.K. McCord, Poincaré-Lefschetz duality for the homology Conley index, Transactions of the AMS 329 (1992), 233–252.

[M] J.T. Montgomery, Cohomology of isolated invariant sets under perturbation, J. Differential Equations 13 (1973), 257–299.

[Mr] M. Mrozek, Leray functor and cohomological Conley index for discrete dynamical systems, Transactions of the AMS 318 (1990), 149–178.

[MMM] C.K. McCord, K. Mischaikow, and M. Mrozek, Zeta functions, periodic trajectories, and the Conley index, J. Differential Equations (to appear).

[N] M. Nagumo, Uber die Differentialgleichung y′′ = f(x, y, y′), Proc. Phys. Math. Soc. Japan Ser. 3 19 (1937), 861–866.

[Pa] J. Palis, On Morse-Smale dynamical systems, Topology 8 (1969), 385–405.

[PaS] J. Palis and S. Smale, Structural stability theorems, Global Analysis (S.- S. Chern and S. Smale, eds.), Proceedings of Symposia in Pure Mathematics, vol. XIV, AMS, Providence, R.I., 1970, pp. 223–231.

[PS] C. Pugh and M. Shub, Linearization of Normally Hyperbolic Diffeomorphisms and Flows, Inventiones math. 10 (1970), 187–198.

[dR] K. de Rezende, Smale flows on the three sphere, Trans. AMS 303 (1987), 283–310.

[R] C. Robinson, Stable manifolds in hamiltonian systems, Hamiltonian Dynamical Systems (K.R. Meyer and D.G. Saari, eds.), Contemporary Mathematics, vol. 81, AMS, Providence, R.I., 1988, pp. 77–97.

[Sl] D. Salamon, Connected simple systems and the Conley index of isolated invariant sets, Trans. AMS 291 (1985), 1–41.

[S] S. Smale, Stable manifolds for differential equations and diffeomorphisms, Annali della Scuola Norm. Sup. - Pisa 17 (1963), 97–116.

[Sm] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Ver-lag, New York Heidelberg Berlin, 1983.

[Sp] E.H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.

[St] N. Steenrod, The Topology of Fibre Bundles, Princeton University Press, Princeton, NJ, 1951.

[Sw] R. Switzer, Algebraic Topology-Homotopy and Homology, Springer-Verlag, New York, 1975.

[WY] F.W. Wilson, Jr. and J.A. Yorke, Lyapunov functions and isolating blocks, J. Differential Equations 13 (1973), 106–123.

10 Westchester Court, Clifton Park, NY 12065 E-mail address: hkurl@math.albany.edu