Singularities of bi-Hamiltonian systems

DOI10.1007/s00220-014-2048-3zbMath1315.37040arXiv1203.3419OpenAlexW3104561255MaRDI QIDQ742863

Anton Izosimov, Alexei V. Bolsinov

Publication date: 19 September 2014

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.3419

zbMATH Keywords

singularitiesintegrabilitybi-Hamiltonian system

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (16)

Jordan-Kronecker invariants of finite-dimensional Lie algebras ⋮ Some remarks about Mishchenko-Fomenko subalgebras ⋮ Finite-dimensional integrable systems: a collection of research problems ⋮ Some remarks on the topology of hyperbolic actions of \(\mathbb{R}^n\) on \(n\)-manifolds ⋮ Jordan-Kronecker invariants of Lie algebra representations and degrees of invariant polynomials ⋮ Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ Open problems in the theory of finite-dimensional integrable systems and related fields ⋮ The \(U(n)\) free rigid body: integrability and stability analysis of the equilibria ⋮ Cotangent models for integrable systems ⋮ Stability in bihamiltonian systems and multidimensional rigid body ⋮ The Adler-van Moerbeke integrable case. Visualization of bifurcations of Liouville tori ⋮ The integrable case of Adler-van Moerbeke. Discriminant set and bifurcation diagram ⋮ Nijenhuis geometry ⋮ Invariant Nijenhuis tensors and integrable geodesic flows ⋮ Bihamilton structure and singularities of momentum mapping for Lagrange top

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bi-Hamiltonian structures and singularities of integrable systems
• Stability in bihamiltonian systems and multidimensional rigid body
• Pencils of complex and real symmetric and skew matrices
• Normal forms for Hamiltonian systems with Poisson commuting integrals - elliptic case
• Spectral theory of a pencil of skew-symmetric differential operators of third order on \(S^ 1\)
• Hamiltonian operators and algebraic structures related to them
• A family of Hamiltonian structures, hierarchy of Hamiltonians, and reduction for first-order matrix differential operators
• Webs, Veronese curves, and bihamiltonian systems
• Note on the integration of Euler's equations of the dynamics of an \(n\)-dimensional rigid body
• On the symplectic structure of the phase space for periodic KdV, Toda, and defocusing NLS
• Bifurcation analysis of the Zhukovskii-Volterra system via bi-Hamiltonian approach
• An elementary proof of the Jordan-Kronecker theorem
• Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems
• 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
• Stability for the korteweg-de vries equation
• A simple model of the integrable Hamiltonian equation
• EULER EQUATIONS ON FINITE-DIMENSIONAL LIE GROUPS
• Wess-Zumino-Witten model based on a nonsemisimple group
• R-matrix theory, formal Casimirs and the periodic Toda lattice
• Singularities, Lax degeneracies and Maslov indices of the periodic Toda chain
• Webs, Lenard schemes, and the local geometry of bi-Hamiltonian Toda and Lax structures

This page was built for publication: Singularities of bi-Hamiltonian systems