Reduction of Polynomial Planar Hamiltonians with Quadratic Unperturbed Part

DOI10.1137/S0036144599362327zbMath0963.37051OpenAlexW1968611432MaRDI QIDQ2706418

Patricia Yanguas, Jesús F. Palacián

Publication date: 19 March 2001

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036144599362327

zbMATH Keywords

Hamiltonianreduced phase spacenormal formformal integrals

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Celestial mechanics (70F15)

Related Items (8)

Singular reduction of resonant Hamiltonians ⋮ Reeb's theorem and periodic orbits for a rotating Hénon-Heiles potential ⋮ Lowering the dimension of polynomial vector fields in R2 and R3 ⋮ Invariant manifolds of an autonomous ordinary differential equation from its generalized normal forms ⋮ Determination of nonlinear stability for low order resonances by a geometric criterion ⋮ Analytical approach for simplifying dynamical systems of polynomial type. ⋮ Equivariant N-Dof Hamiltonians Via Generalized Normal Forms ⋮ Normal forms for Hamiltonian systems in some nilpotent cases

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