Non-integrability of the 1:1:2–resonance

DOI10.1017/S0143385700002649zbMath0537.58026OpenAlexW2148784356MaRDI QIDQ3322894

J. J. Duistermaat

Publication date: 1984

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700002649

zbMATH Keywords

equilibrium pointsresonancehomoclinic orbitsformal integrability

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items

Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems, Nonintegrability of truncated Poincaré-Dulac normal forms of resonance degree two, Hans Duistermaat's contributions to Poisson geometry, Nonintegrability of dynamical systems near degenerate equilibria, On the integrability of twofold 1 : 2 Hamiltonian resonance, Non-integrability of first order resonances in Hamiltonian systems in three degrees of freedom, Chaos in the 1:2:3 Hamiltonian normal form, On resonant classical Hamiltonians with n frequencies, On detuned 1:1:3 Hamiltonian resonance with cases of symmetric cubic and quartic potentials, Local integrability of Poincaré-Dulac normal forms, The coupled 1:2 resonance in a symmetric case and parametric amplification model, Integrability of Hamiltonian systems and Birkhoff normal forms in the simple resonance cases, An asymptotic analysis of the 1:3:4 Hamiltonian normal form, Bifurcations and monodromy of the axially symmetric \(1:1:-2\) resonance, Perturbations of superintegrable systems, Integrability and non-integrability of Hamiltonian normal forms, On perturbed oscillators in 1-1-1 resonance: The case of axially symmetric cubic potentials

Cites Work

• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Homoclinic orbits in Hamiltonian systems
• Asymptotic estimates for spectral functions connected with hypoelliptic differential operators
• Asymptotic analysis of hamiltonian systems