Applications of Nijenhuis geometry: non-degenerate singular points of Poisson-Nijenhuis structures

DOI10.1007/s40879-020-00429-6OpenAlexW3119380732MaRDI QIDQ2095615

Andrey Yu. Konyaev, Vladimir S. Matveev, Alexei V. Bolsinov

Publication date: 17 November 2022

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.04851

zbMATH Keywords

integrable systemssingular pointrecursion operatorNijenhuis tensorbihamiltonian systemscompatible symplectic structures

Mathematics Subject Classification ID

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) Poisson manifolds; Poisson groupoids and algebroids (53D17) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Momentum maps; symplectic reduction (53D20) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Canonical transformations in symplectic and contact geometry (53D22) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (7)

Projective-geometric aspects of bi-Hamiltonian structures of KdV type ⋮ Webs, Nijenhuis operators, and heavenly PDEs ⋮ Nijenhuis geometry. III: \(\mathrm{gl}\)-regular Nijenhuis operators ⋮ Elementary differential singularities of three-dimensional Nijenhuis operators ⋮ Integrating Nijenhuis structures ⋮ Applications of Nijenhuis geometry. III: Frobenius pencils and compatible non-homogeneous Poisson structures ⋮ Applications of Nijenhuis geometry II: maximal pencils of multi-Hamiltonian structures of hydrodynamic type

Cites Work

• Simultaneous local classification of two compatible symplectic forms
• Haantjes manifolds with symmetry
• Bihamiltonian structures and Stäckel separability
• Nijenhuis geometry. II: Left-symmetric algebras and linearization problem for Nijenhuis operators
• Hamiltonian operators of Dubrovin-Novikov type in 2D
• Integrability criteria for systems of nonlinear partial differential equations
• Compatible Poisson brackets of hydrodynamic type
• A simple model of the integrable Hamiltonian equation
• Open problems, questions and challenges in finite- dimensional integrable systems
• Lie Group Representations on Polynomial Rings
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