Birkhoff normalization and superintegrability of Hamiltonian systems

DOI10.1017/S0143385708000965zbMath1194.37086MaRDI QIDQ3650301

Hidekazu Ito

Publication date: 14 December 2009

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

zbMATH Keywords

integrabilityHamiltonian systemsBirkhoff normalization

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

Related Items (5)

Holomorphic normal form of nonlinear perturbations of nilpotent vector fields ⋮ A note on local integrability of differential systems ⋮ A survey on local integrability and its regularity ⋮ Local integrability of Poincaré-Dulac normal forms ⋮ The completely integrable differential systems are essentially linear differential systems

Cites Work

• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Convergence versus integrability in Poincaré-Dulac normal form
• Birkhoff normal form for partial differential equations with tame modulus
• Normal forms for Hamiltonian systems with Poisson commuting integrals - elliptic case
• Some finite dimensional integrable systems and their scattering behavior
• Generalized Liouville method of integration of Hamiltonian systems
• Convergence of Birkhoff normal forms for integrable systems
• Extended integrability and bi-Hamiltonian systems
• Convergence or generic divergence of the Birkhoff normal form
• Action-angle coordinates at singularities for analytic integrable systems
• Integrability of Hamiltonian systems and Birkhoff normal forms in the simple resonance cases
• Holomorphic normalization of Cartan type algebras of singular holomorphic vector fields
• Convergence versus integrability in Birkhoff normal form
• Superintegrable Hamiltonian systems: Geometry and perturbations
• Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung
• Über die Existenz einer Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung
• Sur Certains Systemes Dynamiques Separables
• Singular complete integrability

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