@article{AIHPC_1985__2_5_329_0, author = {Dancer, E. N.}, title = {A new degree for $S^1$-invariant gradient mappings and applications}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {329--370}, publisher = {Gauthier-Villars}, volume = {2}, number = {5}, year = {1985}, mrnumber = {817033}, zbl = {0579.58022}, language = {en}, url = {http://www.numdam.org/item/AIHPC_1985__2_5_329_0/} }
TY - JOUR AU - Dancer, E. N. TI - A new degree for $S^1$-invariant gradient mappings and applications JO - Annales de l'I.H.P. Analyse non linéaire PY - 1985 SP - 329 EP - 370 VL - 2 IS - 5 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPC_1985__2_5_329_0/ LA - en ID - AIHPC_1985__2_5_329_0 ER -
Dancer, E. N. A new degree for $S^1$-invariant gradient mappings and applications. Annales de l'I.H.P. Analyse non linéaire, Tome 2 (1985) no. 5, pp. 329-370. http://www.numdam.org/item/AIHPC_1985__2_5_329_0/
[1] Transversal mappings and flows, Reading, Benjamin, 1967. | MR | Zbl
and ,[2] Lectures on elliptic boundary-value problems, Princeton, Van Nostrand, 1965. | MR | Zbl
,[3] Global bifurcation of periodic orbits, Amer. J. Math., t. 100, 1978, p. 263-292. | MR | Zbl
and ,[4] Non-trivial solutions for a class of non-linear differential equations, Ann. Scuola Norm Sup Pisa, t. 7, 1980, p. 539-693. | Numdam | MR | Zbl
and ,[5] Nonlinearity and functional analysis, New York, Academic Press, 1977. | MR | Zbl
,[6] Analytic functions in topological vector spaces, Studia Math., t. 39, 1971, p. 77-111. | MR | Zbl
and ,[7] Die Losung der Verzweignungsgleichugen für nichtlineare Eigenwert-probleme, Math. Z., t. 127, 1972, p. 105-126. | MR | Zbl
,[8] Introduction to compact transformation groups, New York, Academic Press, 1972. | MR | Zbl
,[9] Opérateurs maximaux monotones, Amsterdam, North Holland, 1973. | MR
,[10] The Fuller index and global bifurcation, J. Diff. Eqns., t. 29, 1978, p. 66-85. | MR | Zbl
and ,[11] Global Hopf bifurcation from a multiple eigenvalue, Nonlinear Analysis, t. 2, 1978, p. 753-763. | MR | Zbl
, and ,[12] Isolated invariant sets and the Morse Index, CBMS regional conferences in mathematics, no. 38, Providence, Amer. Math. Soc., 1978. | MR | Zbl
,[13] Bifurcation from simple eigenvalues, J. Functional Anal., t. 8, 1971, p. 321-340. | MR | Zbl
and ,[14] Bifurcation in real Banach space, Proc. London Math. Soc., t. 23, 1971, p. 699-734. | MR | Zbl
,[15] Global solution branches for positive mappings, Archives Rat. Mech. Anal., t. 52, 1973, p. 181-192. | MR | Zbl
,[16] The G-invariant implicit function theorem in infinite-dimensions, Proc. Royal Soc. Edinburgh, t. 92 A, 1982, p. 13-30. | MR | Zbl
,[17] An implicit function theorem with symmetries and its application to nonlinear eigenvalue problems, Bull. Austral. Math. Soc., t. 21, 1980, p. 81-91. | MR | Zbl
,[18] On the structure of solutions of an equation in catalysis theory when a parameter is large, J. Diff. Eqns., t. 39, 1980, p. 404-437. | MR | Zbl
,[19] On non-radially symmetric bifurcation, J. London Math. Soc., t. 20, 1979, p. 287-292. | Zbl
,[20] On the structure of solutions of nonlinear eigenvalue problems, Indiana Univ. Math. J., t. 23, 1974, p. 1069-1076. | MR | Zbl
,[21] Perturbation of zeros in the presence of symmetries, to appear in J. Austral. Math. Soc. | MR | Zbl
,[22] Remarks on S1-symmetries and a special degree for S1-invariant gradient mappings, submitted.
,[23] Degenerate critical points, homotopy indices and Morse inequalities, J. Reine Ang. Math., t. 350, 1984, p. 1-22. | MR | Zbl
,[24] Generalized cohomology theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Invent. Math., t. 45, 1978, p. 139-174. | MR | Zbl
and ,[25] Perturbation of H-self-adjoint matrices with applications to differential equations, Integral equations and operator theory, t. 5, 1982, p. 718-757. | MR | Zbl
, and ,[26] Bifurcation theory for Fredholm operators, Mem. Amer. Math. Soc., t. 174, 1976. | MR | Zbl
,[27] Perturbation theory for linear operators, Berlin, Springer, 1966. | Zbl
,[28] Degree theory, Cambridge, Cambridge University Press, 1978. | MR | Zbl
,[29] Invariant variational principles, New York, Academic Press, 1977. | MR
,[30] A generalization of multiplicity and the problem of bifurcation, Proc. London Math. Soc., t. 32, 1976, p. 251-278. | MR | Zbl
,[31] Lectures on topics in analysis, Bombay, Tata Institute, 1965. | MR | Zbl
,[32] The fixed point index for locally condensing maps, Ann. Mat. Pura Appl., t. 89, 1971, p. 217-258. | MR | Zbl
,[33] Some global results for nonlinear eigenvalue problems, J. Funct. Anal., t. 7, 1971, p. 487-513. | MR | Zbl
,[34] A bifurcation theorem for potential operators, J. Funct. Anal., t. 25, 1977, p. 412-424. | MR | Zbl
,[35] Group theoretic methods in bifurcation theory, Lecture notes in mathematics, no. 762, Berlin, Springer, 1979. | MR | Zbl
,[36] Lectures on celestial mechanics, Berlin, Springer-Verlag, 1971. | MR | Zbl
and ,[37] Variational methods for the study of nonlinear equations, San Francisco, Holden-Day, 1964.
,[38] Equivariant differential topology, Topology, t. 8, 1969, p. 127-150. | MR | Zbl
,[39] Equilibrium states of an elastic conductor in a magnetic field: a paradigm of bifurcation theory, Trans. Amer. Math. Soc., t. 278, 1983, p. 377-388. | MR | Zbl
,[40] Rotating states of an elastic conductor, preprint. | MR
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