On the prescribed-period problem for autonomous Hamiltonian systems

Electronic Journal of Differential Equations

Volumn 1998, Issue , 1998, Pages 1-9

  Zevin, A A ^a  

^a National Academy of Sciences of Ukraine   (Ukraine)

Author keywords

Autonomous Hamiltonian system; Global analysis; Periodic solutions; Prescribed period problem

Indexed keywords

EID: 0003091661     PISSN: 10726691     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. Ambrosetti A. and G.Mancini: Solutions of minimal period for a class of convex Hamiltonian systems, Math. Ann., 255(1981), 405-421.
2. Aubin J.-P. and I.Ekeland., Applied Nonlinear Analysis, New York, Wiley, 1988.
3. Clarke F.H. and I.Ekeland, Hamiltonian trajectories having prescribed minimal period. Comm. Pure Appl. Math., 33(1980), 103-116.
4. Ekeland I. and H.Hofer, Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems, Invent. Math., 81(1985), 155-188.
5. Girardi M. and M.Matseu, Periodic solutions of convex Hamiltonian systems with a quadratic growth at the origin and superquadratic at infinity, Ann. Mat. Pura. Appl., 147(1987), 21-72.
6. Hartman P., Ordinary differential equations, Wiley, New York, 1964.
7. Krein M.G., Principles of the theory of λ-zones of stability of a canonical system of linear differential equations with periodic coefficients (in Russian), In Memory of A.A.Andronov, Moscow, Izd AN SSSR, (1955), 413-498.
8. Lyapunov A., Probleme generale de la stabilite du mouvement, Ann. Fac. Sci., Toulouse, 2(1907), 203-474.
9. Mallet-Paret J. and J.Yorke, Snakes: oriented families of periodic orbits, their sources, sinks and continuation, J. Diff. Eq., 43(1982), 419-450.
10. Poincaré H., Les methodes nouvelles de la mecanique celeste, 1, Paris, Gauthier-Villars, 1892.
11. Rabinowitz P.H., Critical point theory and applications to differential equations: a survey. Topological Nonlinear Analysis. Progress in Nonlinear Differential Equations and their applications, Birkhauser, Bosotn, 15(1995), 463-513.
12. Van Groesen E.W.C., On small period, large amplitude normal modes of natural Hamiltonian systems, Nonlinear Analysis TMA, 10(1986), No. 1, 41-53.
13. Yakubovitch V.A. and V.M.Starzhinsky, Linear differential equations with periodic coefficients, Wiley, New York, 1980.
14. Yorke J.A., Periods of periodic solutions and the Lipschitz constant, Proc. Amer. Math. Soc., 22(1969), 509-512.
15. Zevin A.A., Qualitative analysis of periodic oscillations in classical autonomous Hamiltonian systems, Int. J. Non-Linear Mech., 28(1993), No. 3, 281-290.
16. Zevin A.A., Nonlocal generalization of the Lyapunov theorem, Nonlinear Analysis TMA, 28(1997), No. 9, 1499-1507.
17. Zevin A.A., On the theory of linear gyroscopic systems, J. Appl. Maths. Mechs., 60(1996), No. 2., 227-232.