On small perturbation of two-dimensional quasi-periodic systems with hyperbolic-type degenerate equilibrium point

DOI10.1016/j.jde.2010.09.030zbMath1217.34076OpenAlexW1968583855MaRDI QIDQ616483

Junxiang Xu

Publication date: 10 January 2011

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

Full work available at URL: https://doi.org/10.1016/j.jde.2010.09.030

zbMATH Keywords

KAM iterationsmall divisorsdegenerate equilibrium pointquasi-periodic systems

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27) Multifrequency systems of ordinary differential equations (34C46)

Related Items

Weakly hyperbolic invariant tori for two dimensional quasiperiodically forced maps in a degenerate case ⋮ Existence of quasi-periodic solutions of fast excited van der Pol-Mathieu-Duffing equation ⋮ On the persistence of degenerate lower-dimensional tori in reversible systems ⋮ Degenerate lower dimensional invariant tori in reversible system ⋮ Paths of real roots for odd-degree polynomials with parameters ⋮ Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems ⋮ Reducibility for a class of two dimensional almost periodic system with quintic real polynomial ⋮ Quasi-periodic solutions for the two-dimensional systems with an elliptic-type degenerate equilibrium point under small perturbations ⋮ Quasi-periodic solutions for differential equations with an elliptic-type degenerate equilibrium point under small perturbations ⋮ Elliptic-type degenerate invariant tori for quasi-periodically forced four-dimensional non-conservative systems ⋮ On small perturbations of a nonlinear periodic system with degenerate equilibrium ⋮ On the reducibility of a class of nonlinear periodic Hamiltonian systems with degenerate equilibrium ⋮ Response solutions of 2-dimensional degenerate systems under quasi-periodic perturbations ⋮ Degenerate lower dimensional tori in reversible systems ⋮ On the persistence of lower-dimensional tori in reversible systems with hyperbolic-type degenerate equilibrium point under small perturbations ⋮ Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems ⋮ On the reducibility of a nonlinear periodic system with degenerate equilibrium ⋮ Construction of response solutions for two classes of quasi-periodically forced four-dimensional nonlinear systems with degenerate equilibrium point under small perturbations ⋮ On small perturbation of four-dimensional quasi-periodic system with degenerate equilibrium point

Cites Work

• Unnamed Item
• Full measure reducibility for generic one-parameter family of quasi-periodic linear systems
• On the reducibility of linear differential equations with quasiperiodic coefficients
• On the reducibility of almost periodic systems of linear differential equations
• A KAM theorem for hyperbolic-type degenerate lower dimensional tori in Hamiltonian systems
• Convergent series expansions for quasi-periodic motions
• A lecture on the classical KAM theorem
• Reducibility for a class of nonlinear quasi-periodic differential equations with degenerate equilibrium point under small perturbation
• Persistence of Floquet invariant tori for a class of non-conservative dynamical systems
• On the reducibility of linear differential equations with quasiperiodic coefficients which are degenerate
• On Quasi-Periodic Perturbations of Elliptic Equilibrium Points
• Unfoldings and bifurcations of quasi-periodic tori