Hamiltonian systems with elliptic periodic orbits

Biancamaria D'Onoforio1, Ivar Ekeland1
1Université de Paris-Dauphine, Place du Marechale de Lattre de Tassigny, 75775 Paris, Cedex 16, France

Tài liệu tham khảo

Bott, 1956, On the iteration of closed geodesics and Sturm intersection theory, Communs pure appl. Math., 9, 176, 10.1002/cpa.3160090204 Clarke, 1981, Periodic solutions of Hamiltonian inclusions, J. diff. Eqns, 40, 1, 10.1016/0022-0396(81)90007-3 Clarke, 1980, Hamiltonian trajectories having prescribed minimal period, Communs pure appl. Math., 33, 103, 10.1002/cpa.3160330202 Conley, 1983, The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold, Inventiones Math., 73, 33, 10.1007/BF01393824 Ekeland, 1984, Une théorie de Morse pour des systémes hamiltoniens convexes, Ann. Inst. H. Poincaré Analyse non Linéaire, 1, 19, 10.1016/S0294-1449(16)30430-9 Ekeland, 1986, An index theory for periodic solutions of convex Hamiltonian systems, Proc. Symp. pure Math., 45, 10.1090/pspum/045.1/843575 Ekeland, 1985, Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems, Inventions Math., 81, 155, 10.1007/BF01388776 EkelandI. & HoferH., Subharmonic solutions for convex nonautonomous Hamiltonian systems, Communs pure appl. Math. (to appear). Ekeland, 1987 Hofer, 1985, A geometric description of the neighbourhood of a critical point given by the mountain pass theorem, J. Lond. math. Soc., 31, 566, 10.1112/jlms/s2-31.3.566 GirardiM. & MatzeuM., Periodic solutions of convex autonomous Hamiltonian systems with a quadratic growth at the origin and superquadratic at infinity, Annali Mat. pura appl. CXLVII, 21-72. Moser, 1977, Proof of a generalized form of a fixed point theorem due to G. D. Birkhoff, 597, 464 Rabinowitz, 1978, Periodic solutions of Hamiltonians systems, Communs pure appl. Math., 31, 157, 10.1002/cpa.3160310203 Takens, 1970, Hamiltonian systems: generic properties of closed orbits and local perturbations, Math. Annln, 188, 304, 10.1007/BF01431464 Viterbo, 1985, IX Viterbo, 1985, Une théorie de Morse pour les systèmes hamiltoniens étoilés, C.R.A.S. Paris, 301, 487 Yakubovich, 1980