Geodesic flows and Neumann systems on Stiefel varieties: geometry and integrability

DOI10.1007/s00209-010-0818-yzbMath1255.53064arXiv1011.1835OpenAlexW1978992889MaRDI QIDQ415489

Yuri N. Fedorov, Božidar Žarko Jovanović

Publication date: 8 May 2012

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.1835

zbMATH Keywords

integrabilitygeodesic flowNeumann systemStiefel variety

Mathematics Subject Classification ID

Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Constrained dynamics, Dirac's theory of constraints (70H45) Geodesic flows in symplectic geometry and contact geometry (53D25) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37Jxx)

Related Items

Extremal curves on Stiefel and Grassmann manifolds ⋮ The Jacobi-Rosochatius problem on an ellipsoid: the Lax representations and billiards ⋮ A multi-parameter family of metrics on Stiefel manifolds and applications ⋮ Discrete geodesic flows on Stiefel manifolds ⋮ Heisenberg model in pseudo-Euclidean spaces. II. ⋮ Continuous and discrete Neumann systems on Stiefel varieties as matrix generalizations of the Jacobi-Mumford systems ⋮ A Lagrangian approach to extremal curves on Stiefel manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Singular Manakov flows and geodesic flows on homogeneous spaces of \(SO(N)\)
• Magnetic flows on homogeneous spaces
• Integrable one-particle potentials related to the Neumann system and the Jacobi problem of geodesic motion on an ellipsoid.
• Finite-zone potentials and integrable systems on a sphere with quadratic potential
• New integrable problem of classical mechanics
• Towards an algebro-geometric interpretation of the Neumann system
• Isospectral Hamiltonian flows in finite and infinite dimensions. I: Generalized Moser systems and moment maps into loop algebras
• Some remarks on the integrability of the equations of motion of a rigid body in an ideal fluid
• The problem of integrable discretization: Hamiltonian approach
• Complete involutive algebras of functions on cotangent bundles of homogeneous spaces
• Nonholonomic LR systems as generalized Chaplygin systems with an invariant measure and flows on homogeneous spaces
• Noncommutative integrability, moment map and geodesic flows
• Einstein metrics on principal fibre bundles
• Isospectral Hamiltonian flows in finite and infinite dimensions. II: Integration of flows
• Integrable anharmonic oscillators on spheres and hyperbolic spaces
• The symmetric representation of the rigid body equations and their discretization
• Integrable flows and Bäcklund transformations on extended Stiefel varieties with application to the Euler top on the Lie group SO(3)
• A variational problem on Stiefel manifolds
• Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups
• INTEGRABILITY OF THE EULER EQUATIONS ASSOCIATED WITH FILTRATIONS OF SEMISIMPLE LIE ALGEBRAS
• The C. Neumann Problem as a Completely Integrable System on an Adjoint Orbit
• Geodesics on quadrics and a mechanical problem of C. Neumann.
• Integrable geodesic flows on homogeneous spaces
• Nahm's Equations and Generalizations of the Neumann System
• Integrable geodesic flows on homogeneous spaces
• Generalized Hamiltonian Dynamics
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura