Global continuation of Lyapunov centre orbits in Hamiltonian systems

Nonlinearity

Volumn 12, Issue 5, 1999, Pages 1339-1349

  Zevin, A A ^a  

^a National Academy of Sciences of Ukraine   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033196547     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/12/5/308     Document Type: Article

References (20)

1. Lyapunov A 1907 Probleme generale de la stabilite du mouvement Ann. Fac. Sci. 2 203-474
2. Zevin A A 1997 Nonlocal generalization of the Lyapunov theorem Nonlinear Anal. Theory Methods Appl. 28 1499-507
3. Mallet-Paret J and Yorke J 1982 Snakes: oriented families of periodic orbits their sources sinks and continuation J. Diff. Eqns 43 419-50
4. Alligood K T and Yorke J 1984 Families of periodic orbits: virtual periods and clobal continuability J. Diff. Eqns 55 59-71
5. Zevin A A 1998 On the prescribed period problem for autonomous Hamiltonian systems Electr. J. Diff. Eqns 5 1-8
6. Yakubovitch V A and Starzhinsky V M 1980 Linear Differential Equations with Periodic Coefficients (New York: Wiley)
7. Rabinowitz P H 1995 Critical point theory and applications to differential equations a survey Topological Nonlinear Analysis. Progress in Nonlinear Differential Equations and their Applications vol 15 (Boston, MA: Birkhauser) pp 463-513
8. Clarke F H and Ekeland I 1980 Hamiltonian trajectories having prescribed minimal period Commun. Pure Appl. Math. 33 103-16
9. Ekeland I and Hofer H 1985 Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems Inv. Math. 81 155-88
10. Ambrosetti A and Mancini G 1981 Solutions of minimal period for a class of convex Hamiltonian systems Math. Ann. 255 405-21
11. Rabinowitz P H 1978 Periodic solutions of Hamiltonian systems Commun. Pure Appl. Math. 31 157-84
12. Ekeland I and Hofer H 1987 Convex Hamiltonian energy surfaces and their closed trajectories Commun. Math. Phys. 113 419-67
13. Ekeland I and Lasry J-M 1980 On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface Ann. Math. 112 283-319
14. Bruno A D 1989 Normalization of a Hamiltonian system near an invariant cycle or torus Russ. Math. Surv. (2) 44 53-89
15. Poincaré H 1892 Les Methodes Nouvelles de la Mecanique Celeste vol 1 (Paris: Gauthier-Villars)
16. Weyl H 1946 The Classical Groups their Invariants and Representations (Princeton, NJ: Princeton University Press)
17. Zevin A A 1998 Stability regions of linear canonical systems with periodic coefficients J. Appl. Math. Mech. 62 37-42
18. Yorke J A 1969 Periods of periodic solutions and the Lipschitz constant Proc. Am. Math. Soc. 22 509-12
19. Meyer K and Hall G 1992 Introduction to Hamiltonian Dynamical Systems and the n-Body Problem (New York: Springer)
20. Weinstein A 1973 Normal modes for nonlinear Hamiltonian systems Inv. Math. 20 47-57