Determination of nonlinear stability for low order resonances by a geometric criterion

DOI10.1134/S1560354712030070zbMath1256.34044OpenAlexW1997522440MaRDI QIDQ691240

Antonio Elipe, Ana I. Pascual, Victor Lanchares

Publication date: 30 November 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354712030070

zbMATH Keywords

normal formsnonlinear stabilityresonances

Mathematics Subject Classification ID

Hamilton's equations (70H05) Stability of solutions to ordinary differential equations (34D20) 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 (1)

Stability of a one-degree-of-freedom canonical system in the case of zero quadratic and cubic part of a Hamiltonian

Cites Work

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• On stability at the Hamiltonian Hopf bifurcation
• The stability of the Lagrange triangular point and a theorem of Arnold
• On the stability of equilibria in two-degrees-of- freedom Hamiltonian systems under resonances
• Reduction of Polynomial Planar Hamiltonians with Quadratic Unperturbed Part
• The critical case of fourth-order resonance in a hamiltonian system with one degree of freedom
• Stability of equilibria and fixed points of conservative systems
• Stability and motion in two degree-of-freedom hamiltonian systems for two-to-one commensurability
• Stability of and motion aboutL 4 at three-to-one commensurability
• Nonlinear stability in resonant cases: A geometrical approach

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