The stability of the equilibrium of planar Hamiltonian and reversible systems

DOI10.1007/s10884-006-9027-0zbMath1103.37037OpenAlexW2081543949MaRDI QIDQ854717

Bin Liu

Publication date: 6 December 2006

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

Full work available at URL: https://doi.org/10.1007/s10884-006-9027-0

zbMATH Keywords

reversible systemsHamiltonian systemsKAM theoryinvariant curvesquasi-periodic functionsstability of the equilibrium

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)

Related Items (10)

The stability of the elliptic equilibrium of planar quasi-periodic Hamiltonian systems ⋮ On the reducibility of analytic quasi-periodic systems with Liouvillean basic frequencies ⋮ On the reducibility of two-dimensional quasi-periodic systems with Liouvillean basic frequencies and without non-degeneracy condition ⋮ The stability of equilibrium of quasi-periodic planar Hamiltonian and reversible systems ⋮ Periodic solutions to superlinear indefinite planar systems: a topological degree approach ⋮ On the reducibility of quasiperiodic linear Hamiltonian systems and its applications in Schrödinger equation ⋮ Quasi-periodic perturbations within the reversible context 2 in KAM theory ⋮ Dynamical stability of quasi-periodic response solutions in planar conservative systems ⋮ On the reducibility of linear quasi-periodic systems with Liouvillean basic frequencies and multiple eigenvalues ⋮ The stability of the equilibrium of the damped oscillator with damping changing sign

Cites Work

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• Stability of zero solutions of essentially nonlinear one-degree-of-freedom Hamiltonian and reversible systems
• The stability of the equilibrium of a conservative system
• Stable and Random Motions in Dynamical Systems
• The stability of the equilibrium of reversible systems
• The Stability of the Equilibrium of a Nonlinear Hill’s Equation
• Parabolic fixed points and stability criteria for nonlinear Hill's equation

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