Response solutions in degenerate oscillators under degenerate perturbations

DOI10.1007/S00023-021-01093-6zbMath1492.34043OpenAlexW3191690688MaRDI QIDQ2068375

Wen Si, Yingfei Yi

Publication date: 19 January 2022

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00023-021-01093-6

zbMATH Keywords

forcing functiondegenerate perturbationperturbed differential equationfrequency vectorquasi-periodically equationresponse solution

Mathematics Subject Classification ID

Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27) Nonautonomous smooth dynamical systems (37C60)

Related Items (7)

Degenerate response tori in Hamiltonian systems with higher zero-average perturbation ⋮ Persistence of degenerate hyperbolic lower-dimensional invariant tori in Hamiltonian systems with Bruno’s conditions ⋮ Response solutions in singularly perturbed, quasi-periodically forced nonlinear oscillators ⋮ Response solutions for degenerate reversible harmonic oscillators with zero-average perturbation ⋮ Response solutions of a class of degenerate quasi-periodic systems with a small parameter ⋮ Response solutions for completely degenerate oscillators under arbitrary quasi-periodic perturbations ⋮ Response solutions of 2-dimensional degenerate systems under quasi-periodic perturbations

Cites Work

• Unnamed Item
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• Resonant tori of arbitrary codimension for quasi-periodically forced systems
• Oscillator synchronisation under arbitrary quasi-periodic forcing
• Umbilical torus bifurcations in Hamiltonian systems
• Local and semi-local bifurcations in Hamiltonian dynamical systems. Results and examples
• The quasi-periodic centre-saddle bifurcation
• A KAM theorem for hyperbolic-type degenerate lower dimensional tori in Hamiltonian systems
• Degenerate lower dimensional invariant tori in reversible system
• Completely degenerate lower-dimensional invariant tori for Hamiltonian system
• On a quasi-periodic Hopf bifurcation
• Quasi-periodic response solutions in forced reversible systems with Liouvillean frequencies
• Whiskered tori for forced beam equations with multi-dimensional Liouvillean frequency
• Degenerate lower-dimensional tori in Hamiltonian systems
• Quasi-periodic motions in families of dynamical systems. Order amidst chaos
• Construction of quasi-periodic response solutions in forced strongly dissipative systems
• Response solutions for quasi-periodically forced harmonic oscillators
• Quasi-periodic motions in strongly dissipative forced systems
• Degenerate lower-dimensional tori under the Bryuno condition
• Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems
• Stoker's Problem for Quasi-periodically Forced Reversible Systems with Multidimensional Liouvillean Frequency
• Completely degenerate responsive tori in Hamiltonian systems
• Response solutions to the quasi-periodically forced systems with degenerate equilibrium: a simple proof of a result of W Si and J Si and extensions
• On the Destruction of Resonant Lagrangean Tori in Hamiltonian Systems
• Resonant motions in the presence of degeneracies for quasi-periodically perturbed systems
• Bifurcations of normally parabolic tori in Hamiltonian systems
• Combination tones for Duffing's equation
• Quasi-periodic solutions of nonlinear ordinary differential equations with small damping

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