Torus Actions and Integrable Systems

Abstract

This is a survey on natural local torus actions which arise in integrable dynamical systems, and their relations with other subjects, including: reduced integrability, local normal forms, affine structures, monodromy, global invariants, integrable surgery, convexity properties of momentum maps, localization formulas, integrable PDEs.

Paper written for a book edited by Bolsinov, Fomenko and Oshemkov

References in corpus (2)

• Two Dimensional Gauge Theories Revisited
• Singular Bohr-Sommerfeld Rules for 2D Integrable Systems

Cited by in corpus (19)

• Symmetries and Integrability
• Contact flows and integrable systems
• Poisson-Lie analogues of spin Sutherland models
• Hidden toric symmetry and structural stability of singularities in integrable systems
• Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds
• Geodesic Flows and Neumann Systems on Stiefel Varieties. Geometry and Integrability
• The Jacobi-Rosochatius problem on an ellipsoid: the Lax representations and billiards
• Structurally stable non-degenerate singularities of integrable systems
• Integrable nonholonomic geodesic flows on compact Lie groups
• Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field
• Integrability of Invariant Geodesic Flows on n-Symmetric Spaces
• Action-Angle variables on Dirac manifolds
• Linearization of proper groupoids
• Integrability of the $n$-dimensional axially symmetric Chaplygin sphere
• Generalized spin Sutherland systems revisited
• Loops of Infinite Order and Toric Foliations
• Bi-Hamiltonian structure of Sutherland models coupled to two $\mathfrak{u}(n{)}^{\ast }$-valued spins from Poisson reduction
• Dynamical complexity and symplectic integrability
• Contact line bundles, foliations, and integrability