Conley, Charles; Zehnder, Eduard Morse-type index theory for flows and periodic solutions for Hamiltonian equations. (English) Zbl 0559.58019 Commun. Pure Appl. Math. 37, 207-253 (1984). Authors’ summary: ”An index theory for flows is presented which extends the classical Morse theory for gradient flows on compact manifolds. The theory is used to prove a Morse-type existence statement for periodic solutions of a time-dependent (periodic in time) and asymptotically linear Hamiltonian equation.” Reviewer: K.Grove Cited in 15 ReviewsCited in 271 Documents MSC: 37G99 Local and nonlocal bifurcation theory for dynamical systems 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces Keywords:index theory; Morse theory; gradient flows; periodic solutions; Hamiltonian equation × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Amann, Math. Z. 169 pp 127– (1979) [2] Amann, Annali Scuola sup. Pisa CI. Sc. Serie IV pp 539– (1980) [3] Amann, Manus. Math. 32 pp 149– (1980) [4] Conley, CBMS Reg. Conf. Series in Math. 38 (1978) · doi:10.1090/cbms/038 [5] Conley, Trans. A. M. S. 158 pp 35– (1971) [6] Spanier, Ann. of Math. 49 pp 407– [7] Algebraic Topology, McGraw-Hill Book Co., Inc., New York, 1966. [8] Smale, Bull. A. M. S. 66 pp 43– (1960) [9] Smoller, Comm. Pure Appl. Math. 27 pp 367– (1974) [10] Churchill, J. Diff. Equations 12 pp 330– (1972) [11] Birkhoff, Acta Math. 47 pp 297– (1925) [12] Brown, Michigan Math. J. 24 pp 21– (1977) [13] Zehnder, Proc. Geometry and Topology, Springer Lecture Notes 597 pp 828– (1977) [14] Chang, Comm. Pure Appl. Math. 34 pp 693– (1981) [15] Rabinowitz, Comm. Pure Appl. Math. 33 pp 609– (1980) [16] Stability of linear Hamiltonian systems with periodic coefficients, IBM Research Report, #RC6610, 1977. [17] Gelfand, Trans. A. M. S. (2) 8 pp 143– (1958) [18] Duistermaat, Adv. in Math. 21 pp 173– (1976) [19] Arnold, Funct. Anal. Appl. 1 pp 1– (1967) [20] Amann, J. of Math. Anal, and Appl. 65 pp 432– (1978) [21] Rybakowski, Trans. A. M. S. 269 pp 351– (1982) [22] Rybakowski, J. Diff. Eqns. 47 pp 66– (1983) [23] Homotopy invariants of repeller–attractor pairs with applications to fast-slow systems, Thesis, University of Wisconsin-Madison, 1979, J. of Diff. Eqns., to appear. [24] and , Forced vibrations of superquadratic Hamiltonian systems, Université P. et M. Curie, 1981, preprint. [25] Jacobowitz, J. Diff. Eqns. 20 pp 37– (1976) [26] Hartmann, J. Diff. Eqns. 26 pp 37– (1977) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.