On the multiplicity of homoclinic orbits on Riemannian manifolds for a class of second order Hamiltonian systems

DOI10.1007/BF01194038zbMath0823.34050MaRDI QIDQ1346253

Fabio Giannoni, Paul H. Rabinowitz

Publication date: 27 March 1995

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

zbMATH Keywords

infinitely many homoclinic orbitssecond order Hamiltonian systems on complete Riemannian manifolds

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Ordinary differential equations and systems on manifolds (34C40) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (11)

Homoclinic orbits on non-compact Riemannian manifolds for second order Hamiltonian systems ⋮ On the existence of homoclinic orbits on Riemannian manifolds ⋮ Connecting orbits near the adiabatic limit of Lagrangian systems with turning points ⋮ Pseudoholomorphic curves and the shadowing lemma ⋮ Multiple brake orbits and homoclinics in Riemannian manifolds ⋮ A multibump construction in a degenerate setting ⋮ On transversal connecting orbits of Lagrangian systems in a nonstationary force field: the Newton-Kantorovich approach ⋮ Connecting orbits of Lagrangian systems in a nonstationary force field ⋮ Doubly asymptotic trajectories of Lagrangian systems in homogeneous force fields ⋮ Symmetrically homoclinic orbits for symmetric Hamiltonian systems ⋮ Homoclinic and heteroclinic orbits for a class of Hamiltonian systems

Cites Work

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• The imbedding problem for Riemannian manifolds
• A variational approach to homoclinic orbits in Hamiltonian systems
• Homoclinic orbits on compact manifolds
• Multiplicity of principal bounce trajectories with prescribed minimal period on Riemannian manifolds
• Homoclinic and heteroclinic orbits for a class of Hamiltonian systems
• Homoclinic Orbits for Second Order Hamiltonian Systems Possessing Superquadratic Potentials
• Category of loop spaces of open subsets in euclidean space
• Homoclinic type solutions for a semilinear elliptic PDE on ℝⁿ
• Homoclinic orbits for a class of Hamiltonian systems

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