A new degree for $S^1$-invariant gradient mappings and applications
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Abraham, 1967
Agmon, 1965
Alexander, 1978, Global bifurcation of periodic orbits, Amer. J. Math., t. 100, 263, 10.2307/2373851
Amann, 1980, Non-trivial solutions for a class of non-linear differential equations, Ann. Scuola Norm Sup Pisa, t. 7, 539
Berger, 1977
Bochnak, 1971, Analytic functions in topological vector spaces, Studia Math., t. 39, 77, 10.4064/sm-39-1-77-112
Bohme, 1972, Die Losung der Verzweignungsgleichugen für nichtlineare Eigenwert-probleme, Math. Z., t. 127, 105, 10.1007/BF01112603
Bredon, 1972
Brezis, 1973
Chow, 1978, The Fuller index and global bifurcation, J. Diff. Eqns., t. 29, 66, 10.1016/0022-0396(78)90041-4
Chow, 1978, Global Hopf bifurcation from a multiple eigenvalue, Nonlinear Analysis, t. 2, 753, 10.1016/0362-546X(78)90017-2
C. Conley, Isolated invariant sets and the Morse Index, CBMS regional conferences in mathematics, no. 38, Providence, Amer. Math. Soc., 1978.
Crandall, 1971, Bifurcation from simple eigenvalues, J. Functional Anal., t. 8, 321, 10.1016/0022-1236(71)90015-2
Dancer, 1971, Bifurcation in real Banach space, Proc. London Math. Soc., t. 23, 699, 10.1112/plms/s3-23.4.699
Dancer, 1973, Global solution branches for positive mappings, Archives Rat. Mech. Anal., t. 52, 181, 10.1007/BF00282326
Dancer, 1982, The G-invariant implicit function theorem in infinite-dimensions, Proc. Royal Soc. Edinburgh, t. 92A, 13, 10.1017/S0308210500019909
Dancer, 1980, An implicit function theorem with symmetries and its application to nonlinear eigenvalue problems, Bull. Austral. Math. Soc., t. 21, 81, 10.1017/S000497270001131X
Dancer, 1979, On non-radially symmetric bifurcation, J. London Math. Soc., t. 20, 287, 10.1112/jlms/s2-20.2.287
Dancer, 1974, On the structure of solutions of nonlinear eigenvalue problems, Indiana Univ. Math. J., t. 23, 1069, 10.1512/iumj.1974.23.23087
E. N. Dancer, Perturbation of zeros in the presence of symmetries, to appear in J. Austral. Math. Soc.
E. N. Dancer, Remarks on S1-symmetries and a special degree for S1-invariant gradient mappings, submitted.
Dancer, 1984, Degenerate critical points, homotopy indices and Morse inequalities, J. Reine Ang. Math., t. 350, 1
Fadell, 1978, Generalized cohomology theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Invent. Math., t. 45, 139, 10.1007/BF01390270
Gokhberg, 1982, Perturbation of H-self-adjoint matrices with applications to differential equations, Integral equations and operator theory, t. 5, 718, 10.1007/BF01694061
Ize, 1976, Bifurcation theory for Fredholm operators, Mem. Amer. Math. Soc., t. 174
Kato, 1966
Lloyd, 1978
Logan, 1977
Magnus, 1976, A generalization of multiplicity and the problem of bifurcation, Proc. London Math. Soc., t. 32, 251, 10.1112/plms/s3-32.2.251
Nussbaum, 1971, The fixed point index for locally condensing maps, Ann. Mat. Pura Appl., t. 89, 217, 10.1007/BF02414948
Rabinowitz, 1971, Some global results for nonlinear eigenvalue problems, J. Funct. Anal., t. 7, 487, 10.1016/0022-1236(71)90030-9
Rabinowitz, 1977, A bifurcation theorem for potential operators, J. Funct. Anal., t. 25, 412, 10.1016/0022-1236(77)90047-7
Siegel, 1971
Vainberg, 1964
Wasserman, 1969, Equivariant differential topology, Topology, t. 8, 127, 10.1016/0040-9383(69)90005-6
Wolfe, 1983, Equilibrium states of an elastic conductor in a magnetic field: a paradigm of bifurcation theory, Trans. Amer. Math. Soc., t. 278, 377, 10.1090/S0002-9947-1983-0697082-3
P. Wolfe, Rotating states of an elastic conductor, preprint.
Dancer, 1980, On the structure of solutions of an equation in catalysis theory when a parameter is large, J. Diff. Eqns., t. 39, 404, 10.1016/0022-0396(80)90107-2
R. Narasimhan, Lectures on topics in analysis, Bombay, Tata Institute, 1965.