The uniqueness of normal forms via Lie transforms and its applications to Hamiltonian systems
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Publication:3703335
DOI10.1007/BF01241045zbMath0581.70009OpenAlexW2060505410MaRDI QIDQ3703335
Publication date: 1985
Published in: Celestial Mechanics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01241045
periodic orbitssingular perturbationuniquenessnormal formsBirkhoff normal formnecessary and sufficient conditionLie transformationrestricted three body problemgeneralized formBirkhoff normalization procedurecritical equilibrium points
Related Items (4)
Non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary ⋮ Dissipative-Hamiltonian decomposition of smooth vector fields based on symmetries ⋮ Invariant manifolds of an autonomous ordinary differential equation from its generalized normal forms ⋮ A note on uniqueness of the normal form for quasi-integrable systems
Cites Work
- The orbit structure of the Hopf bifurcation problem
- On stability of an autonomous Hamiltonian system with two degrees of freedom under first-order resonance
- Lyapunov's center theorem for resonant equilibrium
- Algebraic aspects of perturbation theories
- Normal forms for Hamiltonian systems
- Periodic solutions near a resonant equilibrium of a Hamiltonian system
- An accelerated elimination technique for the solution of perturbed Hamiltonian systems
- An improved transformation-elimination technique for the solution of perturbed Hamiltonian systems
- Canonical transformations depending on a small parameter
- Birkhoff's normalization
- Periodic orbits emanating from a resonant equilibrium
- On a perturbation theory using Lie transforms
- Periodic orbits near ?4 for mass ratios near the critical mass ratio of routh
- Lie transforms and the Hamiltonization of non-Hamiltonian systems
- Perturbation method in the theory of nonlinear oscillations
- Introduction to Non-Linear Mechanics. (AM-11)
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