Symplectic theory of completely integrable Hamiltonian systems
DOI10.1090/S0273-0979-2011-01338-6zbMath1230.37075arXiv1306.0115MaRDI QIDQ3097937
Publication date: 10 November 2011
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1306.0115
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relationships between algebraic curves and integrable systems (14H70) Momentum maps; symplectic reduction (53D20) Global theory of symplectic and contact manifolds (53D35)
Related Items
Cites Work
- Constructing integrable systems of semitoric type
- Kolmogorov condition near hyperbolic singularities of integrable Hamiltonian systems
- Symplectic invariants near hyperbolic-hyperbolic points
- From real affine geometry to complex geometry
- Fixed points and torsion on Kähler manifolds
- The geometry of nondegeneracy conditions in completely integrable systems
- Semitoric integrable systems on symplectic 4-manifolds
- Fractional Hamiltonian monodromy
- Moment polytopes for symplectic manifolds with monodromy
- The moment map for circle actions on symplectic manifolds
- Normal forms for Hamiltonian systems with Poisson commuting integrals - elliptic case
- Symplectically aspherical manifolds
- Quantification géométrique.
- Almost toric symplectic four-manifolds
- Lagrangian 3-torus fibrations
- Le lemme de Morse isochore
- Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. II. Le cas intégrable
- Convexity properties of the moment mapping
- The topology of torus actions on symplectic manifolds. Transl. from the French by the author
- Some remarks on symplectic actions of compact groups
- On Poisson actions of compact Lie groups on symplectic manifolds
- Structure of dynamical systems. A symplectic view of physics. Transl. from the French by C. H. Cushman-de Vries. Transl. ed.: R. H. Cushman a. G. M. Tuynman
- Momentum maps and Hamiltonian reduction
- A note on degenerate corank-one singularities of integrable Hamiltonian systems
- On the quantum expected values of integrable metric forms
- Actions symplectiques de groupes compacts. (Symplectic actions of compact groups)
- A symplectic slice theorem.
- On semifree symplectic circle actions with isolated fixed points
- Riemannian manifolds with uniformly bounded eigenfunctions
- On semi-global invariants for focus-focus singularities
- Singular Lagrangian manifolds and semiclassical analysis.
- Rigid and complete intersection Lagrangian singularities
- Monodromy, diabolic points, and angular momentum coupling
- Kolmogorov condition for integrable systems with focus-focus singularities
- Convexity properties of the moment mapping. III
- Symplectic invariants of some families of Lagrangian \(T^3\)-fibrations
- Convergence versus integrability in Birkhoff normal form
- Topology of symplectic torus actions with symplectic orbits
- Symplectic torus actions with coisotropic principal orbits
- Convexity of multi-valued momentum maps
- Mirror symmetry via logarithmic degeneration data. I
- Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung
- Action-angle Coordinates for Integrable Systems on Poisson Manifolds
- Fixed points of symplectic periodic flows
- Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems
- NON-KAHLER SYMPLECTIC MANIFOLDS WITH TORIC SYMMETRIES
- COMPLEX STRUCTURES ON FOUR-MANIFOLDS WITH SYMPLECTIC TWO-TORUS ACTIONS
- A rigidity theorem for Lagrangian deformations
- Symplectic actions of 2-tori on 4-manifolds
- Reduced phase space and toric variety coordinatizations of Delzant spaces
- Hamiltoniens périodiques et images convexes de l'application moment
- On global action-angle coordinates
- Convexity and Commuting Hamiltonians
- Accessible Sets, Orbits, and Foliations with Singularities
- Sur Certains Systemes Dynamiques Separables
- Typical integrable Hamiltonian systems on a four-dimensional symplectic manifold
- Periodic Hamiltonian flows on four-dimensional manifolds
- Cohomologically Symplectic Spaces: Toral Actions and the Gottlieb Group
- Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $ \mathbb R^2$ in extended neighbourhoods of simple singular points. III. Realization
- A convexity theorem for Poisson actions of compact Lie groups
- Quasimodes and Bohr-Sommerfeld Conditions for the Toeplitz Operators
- The method of loop molecules and the topology of the Kovalevskaya top
- Vanishing twist near focus–focus points
- Singular Bohr–Sommerfeld rules for 2D integrable systems
- Hirzebruch genus of a manifold supporting a Hamiltonian circle action
- Mirror symmetry via logarithmic degeneration data, II
- First Steps Towards a Symplectic Dynamics
- On the Structure of Compact Complex Analytic Surfaces, I
- Quantization and unitary representations
- On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems
- Generalized symplectic rational blowdowns
- Poisson geometry of discrete series orbits, and momentum convexity for noncompact group actions
- 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
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item