A geometric setting for Hamiltonian perturbation theory

DOI10.1090/memo/0727zbMath1003.70002OpenAlexW2068895865MaRDI QIDQ2750966

Anthony D. Blaom

Publication date: 21 October 2001

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/0727

zbMATH Keywords

exponential stabilityHamiltonian perturbation theorymomentum mapsco-adjoint orbitsgeometric formulationEuler-Poinsot rigid bodyNekhoroshev's estimatesnon-abelian symmetry groupsnon-commutatively integrable systems

Mathematics Subject Classification ID

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) Dynamical systems in classical and celestial mechanics (37N05) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09) Nearly integrable Hamiltonian systems, KAM theory (70H08) Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems (70-02)

Related Items (7)

Singular dual pairs. ⋮ Weak dual pairs in Dirac–Jacobi geometry ⋮ Nekhoroshev theorem for perturbations of the central motion ⋮ Exponential stability in the perturbed central force problem ⋮ Superintegrable Hamiltonian systems: Geometry and perturbations ⋮ The frame bundle picture of Gaussian wave packet dynamics in semiclassical mechanics ⋮ Gauge equivalence of Dirac structures and symplectic groupoids

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