On the existence of homoclinic orbits on Riemannian manifolds

DOI10.1017/S0143385700007744zbMath0796.58026OpenAlexW2099273513WikidataQ115336327 ScholiaQ115336327MaRDI QIDQ4290204

Fabio Giannoni

Publication date: 29 September 1994

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700007744

zbMATH Keywords

critical pointshomologyhomoclinic orbitshomotopy

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Ordinary differential equations and systems on manifolds (34C40) Ergodic theory (37A99) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (7)

Pseudoholomorphic curves and multiplicity of homoclinic orbits ⋮ Homoclinic orbits on non-compact Riemannian manifolds for second order Hamiltonian systems ⋮ Connecting orbits near the adiabatic limit of Lagrangian systems with turning points ⋮ 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 ⋮ Symmetrically homoclinic orbits for symmetric Hamiltonian systems ⋮ Structure of Lorentzian tori with a killing vector field

Cites Work

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• Homoclinic orbits in a first order superquadratic Hamiltonian system: Convergence of subharmonic orbits
• On the multiplicity of homoclinic orbits on Riemannian manifolds for a class of second order Hamiltonian systems
• Some results on connecting orbits for a class of Hamiltonian systems
• Morse theory on Hilbert manifolds
• Homoclinic Orbits for Second Order Hamiltonian Systems Possessing Superquadratic Potentials
• Some quasilinear parabolic equations
• Existence of infinitely many homoclinic orbits in Hamiltonian systems

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