Invariant curves of reversible mappings with small twist

DOI10.1007/S10114-004-0316-4zbMath1057.37054OpenAlexW2067581245MaRDI QIDQ1888697

Bin Liu, Jia-Jia Song

Publication date: 26 November 2004

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-004-0316-4

zbMATH Keywords

invariant curvessmall twist theoremreversible mapping

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical aspects of twist maps (37E40)

Related Items (14)

Quasi-periodic solutions for second order differential equation with superlinear asymmetric nonlinearities and nonlinear damping term ⋮ Invariant tori and unboundedness for second order differential equations with asymmetric nonlinearities depending on the derivatives ⋮ Existence of invariant curves for degenerate quasi-periodic reversible mappings ⋮ Existence of invariant curves for degenerate almost periodic reversible mappings ⋮ Invariant curves of quasi-periodic reversible mappings and its application ⋮ Gevrey regularity of invariant curves of analytic reversible mappings ⋮ Lagrangian stability of a class of second-order periodic systems ⋮ The existence of invariant tori and quasiperiodic solutions of the Nosé-Hoover oscillator ⋮ Invariant curves of analytic reversible mappings under Brjuno-Rüssmann's non-resonant condition ⋮ Invariant tori for a reversible oscillator with a nonlinear damping and periodic forcing term ⋮ Invariant curves and boundedness of solutions of a class of reversible systems ⋮ A result on the quasi-periodic solutions of forced isochronous oscillators at resonance ⋮ Boundedness and unboundedness of solutions for reversible oscillators at resonance ⋮ Boundedness of solutions for second order differential equations with asymmetric nonlinearity

Cites Work

• Reversible systems
• Convergent series expansions for quasi-periodic motions
• Invariant Curves of Mappings with Averaged Small Twist
• Stable and Random Motions in Dynamical Systems
• Integrability of hamiltonian systems on cantor sets
• Boundedness in a Piecewise Linear Oscillator and a Variant of the Small Twist Theorem

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