scientific article; zbMATH DE number 885322

zbMath0936.37042arXivmath/0106013MaRDI QIDQ4880507

Nguyen Tien Zung

Publication date: 21 August 1996

Full work available at URL: https://arxiv.org/abs/math/0106013

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

integrable Hamiltonian systemmoment mapArnold-Liouville theorem

Mathematics Subject Classification ID

Related Items (68)

Structurally stable nondegenerate singularities of integrable systems ⋮ Singularities of integrable Hamiltonian systems with the same boundary foliation. An infinite series ⋮ Semitoric integrable systems on symplectic 4-manifolds ⋮ Generating hyperbolic singularities in semitoric systems via Hopf bifurcations ⋮ Invariants of four- and three-dimensional singularities of integrable systems ⋮ Symplectic inverse spectral theory for pseudodifferential operators ⋮ A note on focus-focus singularities ⋮ Universal Lagrangian bundles ⋮ Moduli spaces of semitoric systems ⋮ Realizing integrable Hamiltonian systems by means of billiard books ⋮ Faithful semitoric systems ⋮ Some remarks on the topology of hyperbolic actions of \(\mathbb{R}^n\) on \(n\)-manifolds ⋮ Uncovering fractional monodromy ⋮ Singular levels and topological invariants of Morse Bott integrable systems on surfaces ⋮ Symplectic and inverse spectral geometry of integrable systems: a glimpse and open problems ⋮ Polynomial entropy and polynomial torsion for fibered systems ⋮ Asymptotics of action variables near semi-toric singularities ⋮ Convexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems ⋮ Parabolicity of degenerate singularities in axisymmetric Euler systems with a gyrostat ⋮ Vũ Ngọc's conjecture on focus-focus singular fibers with multiple pinched points ⋮ The affine invariant of proper semitoric integrable systems ⋮ Symplectic linearization of singular Lagrangian foliations in \(M^{4}\). ⋮ Topology of symplectic torus actions with symplectic orbits ⋮ Actions toriques et groupes d'automorphismes de singularités des systèmes dynamiques intégrables. (Torus actions and automorphism groups of singularities of integrable dynamical systems) ⋮ Rigidity of cotangent lifts and integrable systems ⋮ Topology of isoenergy 5-surfaces of a three-axial ellipsoid with a Hooke potential ⋮ Integrable systems and group actions ⋮ Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type ⋮ Foliations of isonergy surfaces and singularities of curves ⋮ Bi-Hamiltonian structures and singularities of integrable systems ⋮ Symplectic invariants of semitoric systems and the inverse problem for quantum systems ⋮ Commuting foliations ⋮ Kolmogorov condition near hyperbolic singularities of integrable Hamiltonian systems ⋮ Symplectic invariants near hyperbolic-hyperbolic points ⋮ Singular fibres of the Gelfand–Cetlin system on MANI( n )* ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ Kolmogorov condition for integrable systems with focus-focus singularities ⋮ Higher index focus-focus singularities in the Jaynes-Cummings-Gaudin model: symplectic invariants and monodromy ⋮ Circle actions in geometric quantisation ⋮ Hamiltonian dynamics and spectral theory for SPIN-oscillators ⋮ From compact semi-toric systems to Hamiltonian \(S^1\)-spaces ⋮ Integrable systems, symmetries, and quantization ⋮ Integrable perturbations of saddle singularities of rank 0 of integrable Hamiltonian systems ⋮ Minimal models of compact symplectic semitoric manifolds ⋮ Geodesics on the ellipsoid and monodromy ⋮ Semiclassical inverse spectral theory for singularities of focus-focus type ⋮ Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems ⋮ Fillable contact structures on torus bundles over circles ⋮ Fractional monodromy: parallel transport of homology cycles ⋮ Constructing integrable systems of semitoric type ⋮ Locally toric manifolds and singular Bohr-Sommerfeld leaves ⋮ Topological classification of Lagrangian fibrations ⋮ Remarks on geometric quantum mechanics ⋮ A conceptual approach to the problem of action-angle variables ⋮ Intersections of Lagrangian submanifolds and the Mel'nikov 1-form ⋮ Symplectic classification of coupled angular momenta ⋮ Saddle singularities of complexity 1 of integrable Hamiltonian systems ⋮ Polynomial entropies for Bott integrable Hamiltonian systems ⋮ A family of semitoric systems with four focus-focus singularities and two double pinched tori ⋮ Singularities of bi-Hamiltonian systems ⋮ Geometry of nondegenerate \({\mathbb R}^n\)-actions on \(n\)-manifolds ⋮ Singular Bohr–Sommerfeld rules for 2D integrable systems ⋮ Geometric quantization via cotangent models ⋮ Symplectic theory of completely integrable Hamiltonian systems ⋮ Complete commutative subalgebras in polynomial poisson algebras: A proof of the Mischenko-Fomenko conjecture ⋮ Hidden toric symmetry and structural stability of singularities in integrable systems ⋮ Asymptotic lattices, good labellings, and the rotation number for quantum integrable systems ⋮ Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bifurcations of invariant manifolds in the generalized Hénon-Heiles system
• Singularities of integrable and near-integrable Hamiltonian systems
• Normal forms for Hamiltonian systems with Poisson commuting integrals - elliptic case
• Le problème général des variables actions-angles. (The general problem of action-angle variables)
• Addendum to ``On the variation in the cohomology of the symplectic form of the reduced phase space
• Monodromy in the champagne bottle
• The topology of torus actions on symplectic manifolds. Transl. from the French by the author
• Reduction of symplectic manifolds with symmetry
• A topological classification of integrable geodesic flows on the two- dimensional sphere with an additional integral quadratic in the momenta
• Algebraic curves and integrable systems: Geodesics of quadrics
• A note on focus-focus singularities
• Monodromy in two degrees of freedom integrable systems
• Decomposition of nondegenerate singularities of integrable Hamiltonian systems
• Singularities of integrable geodesic flows on multidimensional torus and sphere
• Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung
• On the general position property of simple Bott integrals
• Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity
• Hamiltoniens périodiques et images convexes de l'application moment
• On global action-angle coordinates
• COMPATIBLE POISSON BRACKETS ON LIE ALGEBRAS AND COMPLETENESS OF FAMILIES OF FUNCTIONS IN INVOLUTION
• Sur Certains Systemes Dynamiques Separables
• Transversal Homoclinic Orbits in an Integrable System
• Bifurcation diagrams and Fomenko's surgery on Liouville tori of the Kolossoff potential $U=\rho+(1/\rho)-k\cos\phi$
• CLASSIFICATION OF FOUR-DIMENSIONAL INTEGRABLE HAMILTONIAN SYSTEMS AND POISSON ACTIONS OF $ \mathbb{R}^2$ IN EXTENDED NEIGHBORHOODS OF SIMPLE SINGULAR POINTS. II
• On the Volume Elements on a Manifold
• On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems

This page was built for publication: