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Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems. (English) Zbl 0403.57001


MSC:

57S10 Compact groups of homeomorphisms
53C10 \(G\)-structures
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37G99 Local and nonlocal bifurcation theory for dynamical systems

References:

[1] Fadell, E.R., Rabinowitz, P.H.: Bifurcation for odd potential operators and an alternative topological index. J. Functional Analysis,26, 48-67 (1977) · Zbl 0363.47029 · doi:10.1016/0022-1236(77)90015-5
[2] Yang, C.T.: On the theorems of Borsuk-Ulam, Kakutani-Yujobô and Dysin, II. Ann. of Math.62, 271-280 (1955) · Zbl 0067.15202 · doi:10.2307/1969681
[3] Yang, C.T.: On the theorems of Borsuk-Ulam, Kakutani-Yamabe-Yujobô and Dysin, I. Ann. of math.60, 262-282 (1954) · Zbl 0057.39104 · doi:10.2307/1969632
[4] Conner, P.E., Floyd, E.E.: Fixed point free involutions and equivariant maps. Bull. Amer. Math. Soc.66, 416-441 (1960) · Zbl 0106.16301 · doi:10.1090/S0002-9904-1960-10492-2
[5] Holm, P., Spanier, E.H.: Involutions and Fredholm maps. Topology,10, 203-218 (1971) · Zbl 0212.28802 · doi:10.1016/0040-9383(71)90005-X
[6] Coffman, C.V.: A minimum-maximum principle for a class of nonlinear integral equations. J. Analyse Math.22, 391-419 (1969) · Zbl 0179.15601 · doi:10.1007/BF02786802
[7] Rabinowitz, P.H.: Some aspects of nonlinear eigenvalue problems. Rocky Mountain J. Math.3, 161-202 (1973) · Zbl 0255.47069 · doi:10.1216/RMJ-1973-3-2-161
[8] Borel, A.: Princeton, N.J., Seminar on Transformation Groups. Ann. Math. Studies p. 46, Princeton University 1961
[9] Hsiang, W.Y.: Cohomology theory of Topological Transformation Groups. Springer 1975 · Zbl 0429.57011
[10] Weinstein, A.: Normal modes for nonlinear Hamiltonian systems. Inventiones math.20, 47-57 (1973) · Zbl 0264.70020 · doi:10.1007/BF01405263
[11] Moser, J.: Periodic orbits near an equilibrium and a theorem by Alan Weinstein. Comm. Pure Appl. Math.29, 727-747 (1976) · Zbl 0346.34024 · doi:10.1002/cpa.3160290613
[12] Chow, S.N., Mallet-Paret, J.: Periodic solutions near an equilibrium of a non-positive definite Hamiltonian system. Michigan State University (Preprint)
[13] Gleason, A.: Spaces with a compact Lie group of transformations. Proc. Amer. Math. Soc.1, 35-43 (1950) · Zbl 0041.36207 · doi:10.1090/S0002-9939-1950-0033830-7
[14] Dold, A.: Partitions of unity in the theory of fibrations. Ann. of Math.78, 223-255 (1963) · Zbl 0203.25402 · doi:10.2307/1970341
[15] Milnor, J., Stasheff, J.D.: Characteristic Classes. Princeton: University Press 1974 · Zbl 0298.57008
[16] Husemoller, D.: Fibre Bundles. Berlin, Heidelberg, New York: Springer 1975 · Zbl 0307.55015
[17] Spanier, E.: Algebraic Topology, New York, N.Y., McGraw-Hill, 1966 · Zbl 0145.43303
[18] Yang, C.T.: Continuous functions from spheres to Euclidean spaces. Ann. Math.62, 284-292 (1955) · Zbl 0067.15203 · doi:10.2307/1969682
[19] Hirzebruch, F.: Topological Methods in Algebraic Geometry. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0138.42001
[20] Michael, E.: A note on paracompact spaces. Proc. Amer. Math. Soc.4, 831-838 (1953) · Zbl 0052.18701 · doi:10.1090/S0002-9939-1953-0056905-8
[21] Dold, A.: Lectures on Algebraic Topology. Berlin, Heidelberg, New York: Springer 1972 · Zbl 0234.55001
[22] Dugundji, J.: Topology. Boston, Mass.: Allyn and Bacon, 1966
[23] Michael, E.: Another note on paracompact spaces. Proc. Amer. Math. Soc.8, 822-829 (1957) · Zbl 0078.14805 · doi:10.1090/S0002-9939-1957-0087079-9
[24] Bredon, G.E.: Introduction to Compact Transformation Groups. London, New York: Academic Press 1972 · Zbl 0246.57017
[25] Steenrod, N.E.: The Topology of Fibre Bundles. Princeton: University Press 1951 · Zbl 0054.07103
[26] Palais, R.S.: The Classification ofG-Spaces. AMS Memoir, No. 36 (1960) · Zbl 0119.38403
[27] Conner, P.E., Floyd, E.E.: Orbit spaces of circle groups of transformations. Ann. Math.67, 90-98 (1958) · Zbl 0079.38903 · doi:10.2307/1969928
[28] Nemytskii, V.V., Stepanov, V.V.: Qualitative theory of differential equations. Princeton: University Press 1960 · Zbl 0089.29502
[29] Weinstein, A.: Lagrangian submanifolds and Hamiltonian systems. Ann. Math.98, 377-410 (1973) · Zbl 0271.58008 · doi:10.2307/1970911
[30] Rabinowitz, P.H.: Variational methods for nonlinear eigenvalue problems. Proc. Sym. on Eigenvalues of Nonlinear Problems, pp. 141-195. Rome: Edizioni Cremonese 1974 · Zbl 0278.35040
[31] Clark, D.C.: A variant of the Ljusternik-Schnirelman theory. Indiana Univ. Math. J.22, 65-74 (1972) · Zbl 0228.58006 · doi:10.1512/iumj.1972.22.22008
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