References
Benci, V.: On critical point theory for indefinite functionals in the presence of symmetries. Trans. Am. Math. Soc.274, 533–572 (1982)
Berestycki, H., Lasry, J.M., Mancini, G., Ruf, B.: Existence of multiple periodic orbits on star-shaped Hamiltonian surfaces. Commun. Pure. Appl. Math.38, 253–289 (1985)
Bögle, J.G.: Indextheorien zur Existenz von periodischen Lösungen Hamiltonscher Systeme. Thesis, Ludwig-Maximilians-Universität München, 1987
Ekeland, I., Lasry, J.M.: On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface. Ann. Math.112, 283–319 (1980)
Girardi, M.: Multiple orbits for Hamiltonian systems on starshaped surfaces with symmetries. Ann. Inst. Henri Poincaré Nouv. Ser. Sect.B1, 285–294 (1984)
Girardi, M., Matzeu, M.: Solutions of minimal period for a class of noncovex Hamiltonian systems and applications to the fixed energy problem. Nonl. Anal., Theory Methods Appl.10, 371–382 (1986)
Guillemin, V., Pollack, A.: Differential topology. Englewoods Cliffs. Prentice-Hall 1974
Hofer, H., Zehnder, E.: Periodic solutions on hypersurfaces and a result by C. Viterbo. Invent. Math.90, 1–9 (1987)
Lloyd, N.G.: Degree theory. Cambridge: Cambridge University Press 1978
Michalek, R: A Zp Borsuk-Ulam theorem and index theory with a multiplicity result. Preprint
Nirenberg, L.: Comments on nonlinear problems. Le Matematiche36, 109–119 (1981)
Rabinowitz, P.H.: Periodic solutions of Hamiltonian systems. Commun. Pure Appl. Math.31, 157–184 (1978)
Rabinowitz, P.H.: Minimax methods in critical point theory with applications to differential equations. CBMS 65. Am. Math. Soc., Providence, R.I. 1986
Rabinowitz, P.H.: On the existence of periodic solutions for a class of symmetric Hamiltonian systems. Nonl. Anal., Theory Methods Appl.11, 599–611 (1987)
Rabinowitz, P.H: On a theorem of Hofer and Zehnder. In: Periodic solutions of Hamiltonian systems and related topics. (to appear)
Seifert, H.: Periodische Bewegungen mechanischer Systeme. Math. Z.51, 197–216 (1948)
Szulkin, A.: Critical point theory of Ljusternik-Schnirelmann type and applications to partial differential equations. In: Séminaire de Mathématiques Supérieures, Les Presses de l'Université de Montréal. (to appear)
Tarantello, G: Subharmonic solutions for Hamiltonian, systems via a Zp pseudoindex theory Preprint
Groesen, E.W.C. van: Existence of multiple normal mode trajectories on convex energy surfaces of even, classical Hamiltonian systems. J. Differ. Equations57, 70–89 (1985)
Viterbo, C.: A proof of Weinstein's conjecture inR 2n. Ann. Inst. Henri Poincaré Nouv Sér. Sect.B4, 337–356 (1987)
Wang, Z.Q.: A Z p Borsuk-Ulam theorem. Preprint
Weinstein, A.: Periodic orbits for convex hamiltonian systems. Ann. Math.108, 507–518 (1978)
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Supported in part by the Swedish Natural Science Research Council
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Szulkin, A. An index theory and existence of multiple brake orbits for star-shaped Hamiltonian systems. Math. Ann. 283, 241–255 (1989). https://doi.org/10.1007/BF01446433
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DOI: https://doi.org/10.1007/BF01446433