Abstract
The present work has its origin in a recent paper of Peixoto and Thom [7].
We begin by reformulating the Theorem of this paper (p. 639) in a way that renders its statement and proof more simple and conceptual. This is done by the use of the concept of graph of a foliation, introduced by Thom [9, p. 173] as follows: The graph of a foliated manifold F is the set of points (p, q) ∈ F ×F such that p and q are on the same leaf.
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References
Brillouin, L., Wave Propagation in Periodic Structures. 2nd ed. Dover, New York (1953).
Busch, G. and Schade, H., Lectures on Solid State Physics. Pergamon Press, Oxford (1976).
Dieudonné, J. Treatise on Analysis. Academic Press, New York (1974), Volume 4.
Goresky, M. and MacPherson, R., Stratified Morse Theory. Springer-Verlag, Berlin (1988).
Hardy, G.H. and Wright, E.M., An Introduction to the Theory of Numbers. 5th ed. Clarendon Press, Oxford (1989).
Peixoto, M.M., On a Generic Theory of End Point Boundary Value Problems. An. Acad. Bras. Cienc. 41 (1969), 1–6.
Peixoto, M.M. and Thom, R., Le point de vue énumératif dans les problèmes aux limites pour les équations différentielles ordinaires. C.R. Acad. Se. Paris, t. 303, Série I, n° 13 (1986), 629–632 and t. 307, Série I (1988), 197–198 (Erratum) and t. 303, Série I, n° 14 (1986), 693–698.
Smale, S., An infinite dimensional version of Sard’s theorem. Amer. J. Math. 87 (1965), 861–866.
Thom, R., Généralisation de la Théorie de Morse aux Variétés Feuilletées. Ann. Inst. Fourier, Grenoble 14 (1964), 173–190.
Winkelnkemper, H.E., The Graph of a Foliation. Ann. Glob. Analysis and Geometry, v. 1, n. 3 (1983), 51–75.
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Kupka, I.A.K., Peixoto, M.M. (1993). On the Enumerative Geometry of Geodesics. In: Hirsch, M.W., Marsden, J.E., Shub, M. (eds) From Topology to Computation: Proceedings of the Smalefest. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2740-3_24
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