Homoclinic, heteroclinic, and periodic orbits for a class of indefinite Hamiltonian systems

DOI10.1007/BF01457066zbMath0569.70017MaRDI QIDQ1060877

Helmut Hofer, John F. Toland

Publication date: 1984

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/182927

zbMATH Keywords

inner productexistence of periodic orbitpartial orderingnonlinear water wavessymmetric linear operatorEuclidian n-spaceexistence of heteroclinic orbitexistence of homoclinic orbitindefinite Hamiltonian systemsmonotonicity property of the orbits

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Hamilton's equations (70H05) Dynamical systems and ergodic theory (37-XX)

Related Items (19)

Geometry of spaces with the Jacobi metric ⋮ Periodic solutions for a class of Lorenz-Lagrangian systems ⋮ Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system ⋮ Homoclinic orbits in the dynamic phase-space analogy of an elastic strut ⋮ A necessary geometric condition for the existence of certain homoclinic orbits ⋮ Periodic and homoclinic orbits for Lorentz-Lagranian systems via variational methods ⋮ Homoclinic bifurcation at resonant eigenvalues ⋮ Strictly ordered minimal subsets of a class of convex monotone skew-product semiflows. ⋮ Heteroclinic cycles arising in generic unfoldings of nilpotent singularities ⋮ Global uniqueness of homoclinic orbits for a class of fourth order equations ⋮ Shooting methods and topological transversality ⋮ Galerkin's method, monotonicity and linking for indefinite Hamiltonian systems with bounded potential energy ⋮ Points of egress in problems of Hamiltonian dynamics ⋮ Closed characteristics on non-compact hypersurfaces in \(\mathbb {R}^{2n}\) ⋮ Bifurcation of a reversible Hamiltonian system from a fixed point with fourfold eigenvalue zero ⋮ Pulse-like spatial patterns described by higher-order model equations ⋮ A class of periodic orbits in classical mechanics ⋮ Uniqueness and a priori bounds for certain homoclinic orbits of a Boussinesq system modelling solitary water waves ⋮ Abstract competitive systems and orbital stability in $\mathbf{{\mathbb R}^3}$

Cites Work

• Unnamed Item
• Uniqueness and a priori bounds for certain homoclinic orbits of a Boussinesq system modelling solitary water waves
• Periodic solutions of Hamiltonian system on a prescribed energy surface
• On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface
• Periodic orbits for convex hamiltonian systems
• Periodische Bewegungen mechanischer Systeme
• Solitary wave solutions for a model of the two-way propagation of water waves in a channel

This page was built for publication: Homoclinic, heteroclinic, and periodic orbits for a class of indefinite Hamiltonian systems