Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-30T15:55:40.591Z Has data issue: false hasContentIssue false
  • English
  • Français

Heteroclinics for a reversible Hamiltonian system

Published online by Cambridge University Press:  19 September 2008

Paul H. Rabinowitz
Paul H. Rabinowitz
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper uses an elementary variational argument to establish the existence of solutions heteroclinic to a pair of periodic orbits for a class of Hamiltonian systems including Hamiltonians of multiple pendulum type.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 4 , December 1994 , pp. 817 - 829
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Rabinowitz, P.H.. On a class of functional invariant under a ℤn action. Trans. Amer. Math. Soc. 310 (1988), 303–311.Google Scholar
[2]Guckenheimer, J. and Holmes, P.J.. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag: Berlin, 1983.Google Scholar
[3]Kirchgraber, U. and Stoffer, D.. Chaotic behavior in simple dynamical systems. SIAM Rev. 32 (1990), 424–452.CrossRefGoogle Scholar
[4]Rabinowtiz, P.H.. Periodic and heteroclinic orbits for a periodic Hamiltonian system. Ann. Inst. H. Poincaré—Analyse nonlineaire 6 (1989), 331–346.CrossRefGoogle Scholar
[5]Rabinowitz, P.H.. A variational approach to heteroclinic orbits for a class of Hamiltonian systems. Frontiers in Pure and Applied Math. (Dautray, R., ed.) (1991), 267–278.Google Scholar
[6]Rabinowitz, P.H.. Some recent results on heteroclinic and other connecting orbits of Hamiltonian systems. Proc. Conf. on Variational Methods in Hamiltonian Systems and Elliptic Equations L'Aquila. To appear.Google Scholar
[7]Bolotin, S.V.. The existence of homoclinic motions. Vestnik Moskovskogo Universitita, Matematica 38 (1983), 98–103.Google Scholar
[8]Bolotin, S.V.. Homoclinic orbits to invariant tori of symplectic diffeomorphisms and Hamiltonian systems. Preprint.Google Scholar
[9]Offin, D.. Private communication.Google Scholar
[10]Kozlov, V.V.. Calculus of variations in the large and classical mechanics. Russ. Math. Surv. 40 (1985), 37–71.CrossRefGoogle Scholar
[11]Rabinowtiz, P.H. and Tanaka, K.. Some results on connecting orbits for a class of Hamiltonian systems. Math. Z. 206 (1991), 473–499.CrossRefGoogle Scholar