Branches of forced oscillations for periodically perturbed second-order autonomous ODEs on manifolds

DOI10.1006/jdeq.1998.3557zbMath0929.34032OpenAlexW2057764274MaRDI QIDQ1288864

Massimo Furi, Marco Spadini

Publication date: 16 January 2000

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1998.3557

zbMATH Keywords

bifurcationdifferentiable manifoldstopological degreeforced oscillationsperiodic perturbationsparametrized second-order differential equations

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Periodic and quasi-periodic flows and diffeomorphisms (37C55)

Related Items (6)

Branches of forced oscillations induced by a delayed periodic force ⋮ Forced oscillations on manifolds and multiplicity results for periodically perturbed autonomous systems ⋮ Multiplicity of forced oscillations for the spherical pendulum acted on by a retarded periodic force ⋮ Branches of forced oscillations in degenerate systems of second-order ODEs ⋮ Branches of index-preserving solutions to systems of second order ODEs ⋮ Periodic perturbations of constrained motion problems on a class of implicitly defined manifolds

Cites Work

• A continuation principle for periodic solutions of forced motion equations on manifolds and applications to bifurcation theory
• A continuation principle for forced oscillations on differentiable manifolds
• Multiplicity of forced oscillations for the spherical pendulum
• Differential Topology
• On the set of harmonic solutions of periodically perturbed autonomous differential equations on manifolds
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