Article PDF
Avoid common mistakes on your manuscript.
References
Fadell, E.R., Rabinowitz, P.H.: Bifurcation for odd potential operators and an alternative topological index. J. Functional Analysis,26, 48–67 (1977)
Yang, C.T.: On the theorems of Borsuk-Ulam, Kakutani-Yujobô and Dysin, II. Ann. of Math.62, 271–280 (1955)
Yang, C.T.: On the theorems of Borsuk-Ulam, Kakutani-Yamabe-Yujobô and Dysin, I. Ann. of math.60, 262–282 (1954)
Conner, P.E., Floyd, E.E.: Fixed point free involutions and equivariant maps. Bull. Amer. Math. Soc.66, 416–441 (1960)
Holm, P., Spanier, E.H.: Involutions and Fredholm maps. Topology,10, 203–218 (1971)
Coffman, C.V.: A minimum-maximum principle for a class of nonlinear integral equations. J. Analyse Math.22, 391–419 (1969)
Rabinowitz, P.H.: Some aspects of nonlinear eigenvalue problems. Rocky Mountain J. Math.3, 161–202 (1973)
Borel, A.: Princeton, N.J., Seminar on Transformation Groups. Ann. Math. Studies p. 46, Princeton University 1961
Hsiang, W.Y.: Cohomology theory of Topological Transformation Groups. Springer 1975
Weinstein, A.: Normal modes for nonlinear Hamiltonian systems. Inventiones math.20, 47–57 (1973)
Moser, J.: Periodic orbits near an equilibrium and a theorem by Alan Weinstein. Comm. Pure Appl. Math.29, 727–747 (1976)
Chow, S.N., Mallet-Paret, J.: Periodic solutions near an equilibrium of a non-positive definite Hamiltonian system. Michigan State University (Preprint)
Gleason, A.: Spaces with a compact Lie group of transformations. Proc. Amer. Math. Soc.1, 35–43 (1950)
Dold, A.: Partitions of unity in the theory of fibrations. Ann. of Math.78, 223–255 (1963)
Milnor, J., Stasheff, J.D.: Characteristic Classes. Princeton: University Press 1974
Husemoller, D.: Fibre Bundles. Berlin, Heidelberg, New York: Springer 1975
Spanier, E.: Algebraic Topology, New York, N.Y., McGraw-Hill, 1966
Yang, C.T.: Continuous functions from spheres to Euclidean spaces. Ann. Math.62, 284–292 (1955)
Hirzebruch, F.: Topological Methods in Algebraic Geometry. Berlin, Heidelberg, New York: Springer 1966
Michael, E.: A note on paracompact spaces. Proc. Amer. Math. Soc.4, 831–838 (1953)
Dold, A.: Lectures on Algebraic Topology. Berlin, Heidelberg, New York: Springer 1972
Dugundji, J.: Topology. Boston, Mass.: Allyn and Bacon, 1966
Michael, E.: Another note on paracompact spaces. Proc. Amer. Math. Soc.8, 822–829 (1957)
Bredon, G.E.: Introduction to Compact Transformation Groups. London, New York: Academic Press 1972
Steenrod, N.E.: The Topology of Fibre Bundles. Princeton: University Press 1951
Palais, R.S.: The Classification ofG-Spaces. AMS Memoir, No. 36 (1960)
Conner, P.E., Floyd, E.E.: Orbit spaces of circle groups of transformations. Ann. Math.67, 90–98 (1958)
Nemytskii, V.V., Stepanov, V.V.: Qualitative theory of differential equations. Princeton: University Press 1960
Weinstein, A.: Lagrangian submanifolds and Hamiltonian systems. Ann. Math.98, 377–410 (1973)
Rabinowitz, P.H.: Variational methods for nonlinear eigenvalue problems. Proc. Sym. on Eigenvalues of Nonlinear Problems, pp. 141–195. Rome: Edizioni Cremonese 1974
Clark, D.C.: A variant of the Ljusternik-Schnirelman theory. Indiana Univ. Math. J.22, 65–74 (1972)
Author information
Authors and Affiliations
Additional information
This research was sponsored in part by the Office of Naval Research under Contract No. N00014-76-C-0300, by the U.S. Army under Contract No. DAAG2-75-C-0024, and in part by the National Science Foundation under Grant No. NSF MCS76-06373. Any reproduction in part or in full for the purposes of the U.S. Government is permitted
Rights and permissions
About this article
Cite this article
Fadell, E.R., Rabinowitz, P.H. Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems. Invent Math 45, 139–174 (1978). https://doi.org/10.1007/BF01390270
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01390270