Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T13:03:57.808Z Has data issue: false hasContentIssue false
  • English
  • Français

A priori bounds for periodic solutions of a class of Hamiltonian systems

Published online by Cambridge University Press:  10 December 2009

Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper concerns estimates for periodic solutions of a very general class of Hamiltonian systems of prescribed energy. The estimtes are a priori upper and lower bounds for the action integral in terms of the period.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Volume 8: Charles Conley Memorial Issue , December 1988 , pp. 27 - 31
Copyright
Copyright © Cambridge University Press 1988

References

REFERENCES

Ambrosetti, A. & Mancini, G.. On a theorem by Ekeland and Lasry concerning the number of periodic Hamiltonian trajectories. J. Differential Equations 43 (1981), 1–6.Google Scholar
Benci, V.. Closed geodesies for the Jacobi metric and periodic solutions of prescribed energy of natural Hamiltonian systems. Ann. Inst. H. Poincaré, Anal, nonlin.Google Scholar
Berestycki, H., Lasry, J. M., Mancini, G. and Ruf, B.. Existence of multiple periodic orbits on star-shaped Hamiltonian surfaces. Comm. Pure Appl. Math. 38 (1985), 253–290.Google Scholar
Clarke, F.. A classical variational principle for periodic Hamiltonian trajectories. Proc. Am. Math. Soc. 76 (1979), 186–188.Google Scholar
Ekeland, I. & Lasry, J. M.. On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface. Ann. Math. 112 (1980), 283–319.10.2307/1971148Google Scholar
Girardi, M.. Multiple orbits for Hamiltonian systems on starshaped surfaces with symmetries. Ann. Inst. H. Poincaré, Anal. nonlin. 1 (1984), 285–294.10.1016/S0294-1449(16)30423-1Google Scholar
Gluck, H. & Ziller, W.. Existence of periodic solutions of conservative systems. Seminar on Minimal Submanifolds. Princeton University Press (1983), 65–98.Google Scholar
van Groesen, E. W. C.. Existence of multiple normal mode trajectories on convex energy surfaces of even classical Hamiltonian systems. j. Differential Equations 57 (1985), 70–89.Google Scholar
Hayashi, K.. Periodic solution of classical Hamiltonian systems. Tokyo J. Math. 6 (1983), 473–486.10.3836/tjm/1270213886Google Scholar
Hofer, H.. A simple proof for a result of I. Ekeland and J. M. Lasry concerning the number of periodic Hamiltonian trajectories on a prescribed energy surface. Preprint.Google Scholar
Palais, R. S.. Critical point theory and the minimax principle. Proc. Symp. Pure Math. 15. AMS, Providence, RI (1970), 185–212.Google Scholar
Rabinowitz, P. H.. Periodic solutions of Hamiltonian systems. Comm. Pure Appl. Math. 31 (1978), 157–184.10.1002/cpa.3160310203Google Scholar
Rabinowitz, P. H.. Periodic solutions of a Hamiltonian system on a prescribed energy surface. J. Differential Equations 33 (1979), 336–352.10.1016/0022-0396(79)90069-XGoogle Scholar
Rabinowitz, P. H.. On the existence of periodic solutions for a class of symmetric Hamiltonian systems. J. Nonlin. Anal. - TMA.Google Scholar
Ruiz, O. R.. Existence of brake orbits in Finsler mechanical systems. Springer Lecture Notes in Mathematics 597 (1977), 542–567.Google Scholar
Seifert, H.. Periodische Bewegungen mechanischen Systeme. Math. Z. 51 (1948), 197–216.10.1007/BF01291002Google Scholar
Weinstein, A.. Periodic orbits for convex Hamiltonian systems. Ann. Math. 108 (1978), 507–518.Google Scholar