The affine invariant of proper semitoric integrable systems

DOI10.1088/1361-6544/aa8aeczbMath1392.37046OpenAlexW2963368173MaRDI QIDQ4597515

San Vũ Ngoc, Álvaro Pelayo, Tudor S. Ratiu

Publication date: 13 December 2017

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6544/aa8aec

zbMATH Keywords

moment mapspherical pendulumLagrangian fibrationsemitoric integrable system

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Symplectic and contact topology in high or arbitrary dimension (57R17) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Moduli problems for differential geometric structures (58D27) Momentum maps; symplectic reduction (53D20) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Group actions on manifolds and cell complexes in low dimensions (57M60)

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Cites Work

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• Generating hyperbolic singularities in semitoric systems via Hopf bifurcations
• Circle-valued momentum maps for symplectic periodic flows
• Smooth normal forms for integrable Hamiltonian systems near a focus-focus singularity
• First steps in symplectic and spectral theory of integrable systems
• On exotic Lagrangian tori in \(\mathbb{CP}^{2}\)
• From compact semi-toric systems to Hamiltonian \(S^1\)-spaces
• Constructing integrable systems of semitoric type
• Hamiltonian dynamics and spectral theory for SPIN-oscillators
• Semitoric integrable systems on symplectic 4-manifolds
• Moment polytopes for symplectic manifolds with monodromy
• Normal forms for Hamiltonian systems with Poisson commuting integrals - elliptic case
• Almost toric symplectic four-manifolds
• On the variation in the cohomology of the symplectic form of the reduced phase space
• Convexity properties of the moment mapping
• Moment maps and combinatorial invariants of Hamiltonian \(T^ n\)-spaces
• Non-Abelian convexity by symplectic cuts
• Sign of the monodromy for Liouville integrable systems
• On semi-global invariants for focus-focus singularities
• Monodromy, diabolic points, and angular momentum coupling
• Fiber connectivity and bifurcation diagrams of almost toric integrable systems
• Symplectic invariants and Hamiltonian dynamics
• Mirror symmetry via logarithmic degeneration data. I
• Topology and mechanics. I
• Topology and mechanics. II: The planar \(n\)-body problem
• Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems
• Symplectic Origami
• Symplectic theory of completely integrable Hamiltonian systems
• A semi-classical study of the Jaynes–Cummings model
• Hamiltoniens périodiques et images convexes de l'application moment
• Convexity and Commuting Hamiltonians
• Sur Certains Systemes Dynamiques Separables
• Periodic Hamiltonian flows on four-dimensional manifolds
• Hamiltonian torus actions on symplectic orbifolds and toric varieties
• Quantum states in a champagne bottle
• The Radiance Obstruction and Parallel Forms on Affine Manifolds