Superintegrable Hamiltonian systems: Geometry and perturbations

DOI10.1007/s10440-005-1139-8zbMath1073.37069OpenAlexW2113557458MaRDI QIDQ2487195

Francesco Fassoò

Publication date: 18 August 2005

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: http://infoscience.epfl.ch/record/125828

zbMATH Keywords

rigid bodyHamiltonian perturbation theorysuperintegrabilitydual pairs

Mathematics Subject Classification ID

Related Items (41)

Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds ⋮ MOMENTUM MAPS, INDEPENDENT FIRST INTEGRALS AND INTEGRABILITY FOR CENTRAL POTENTIALS ⋮ SUPERINTEGRABLE HAMILTONIAN SYSTEMS WITH NONCOMPACT INVARIANT SUBMANIFOLDS: KEPLER SYSTEM ⋮ A Hamilton-Jacobi theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds ⋮ Unnamed Item ⋮ Hamiltonian and reversible systems with smooth families of invariant tori ⋮ Singular reduction of resonant Hamiltonians ⋮ Quantization of noncommutative completely integrable Hamiltonian systems ⋮ Globally superintegrable Hamiltonian systems ⋮ Noncommutative integrability from classical to quantum mechanics ⋮ The degenerate C. Neumann system. I: Symmetry reduction and convexity ⋮ Taylor series and twisting-index invariants of coupled spin-oscillators ⋮ Linearity of minimally superintegrable systems in a static electromagnetic field ⋮ Poisson and symplectic reductions of 4–DOF isotropic oscillators. The van der Waals system as benchmark ⋮ Quasiperiodic version of Gordon's theorem ⋮ On the geometric and analytical properties of the anharmonic oscillator ⋮ GEOMETRICAL ASPECTS OF INTEGRABLE SYSTEMS ⋮ Lagrangian multiforms on Lie groups and non-commuting flows ⋮ Nekhoroshev theorem for perturbations of the central motion ⋮ Necessary conditions for super-integrability of Hamiltonian systems ⋮ Some ring-shaped potentials as a generalized 4-D isotropic oscillator. Periodic orbits ⋮ Coupling linearity and twist: an extension of the Poincaré-Birkhoff theorem for Hamiltonian systems ⋮ A Lagrangian fibration of the isotropic 3-dimensional harmonic oscillator with monodromy ⋮ Transformation of the Stäckel matrices preserving superintegrability ⋮ The \(d\)-dim oscillator and Kepler problems. The potential \(1/x ^{2}\) ⋮ Geodesic flow on three-dimensional ellipsoids with equal semi-axes ⋮ Integrable almost-symplectic Hamiltonian systems ⋮ Exponential stability in the perturbed central force problem ⋮ Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry ⋮ TIME-DEPENDENT SUPERINTEGRABLE HAMILTONIAN SYSTEMS ⋮ Completely integrable Hamiltonian systems with weak Lyapunov instability or isochrony ⋮ INTEGRABILITY AND SUPERINTEGRABILITY OF TODA SYMPLECTIC MAP WITH MULTIPLE EIGENPARAMETERS ⋮ Hamiltonian monodromy via geometric quantization and theta functions ⋮ No monodromy in the champagne bottle, or singularities of a superintegrable system ⋮ An Overview on the Nekhoroshev Theorem ⋮ The Hamilton-Jacobi equation, integrability, and nonholonomic systems ⋮ Birkhoff normalization and superintegrability of Hamiltonian systems ⋮ Hamiltonian systems admitting a Runge-Lenz vector and an optimal extension of Bertrand's theorem to curved manifolds ⋮ Perturbations of superintegrable systems ⋮ Stratified Lie systems: theory and applications ⋮ Superintegrability of left-invariant sub-Riemannian structures on unimodular three-dimensional Lie groups

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