Haantjes algebras of classical integrable systems

DOI10.1007/s10231-021-01107-4OpenAlexW3167867148MaRDI QIDQ2118006

Piergiulio Tempesta, Giorgio Tondo

Publication date: 22 March 2022

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.5118

zbMATH Keywords

integrable systemssymplectic manifoldsHaantjes tensors

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) KdV equations (Korteweg-de Vries equations) (35Q53) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37)

Related Items

Generically, Arnold-Liouville systems cannot be bi-Hamiltonian, Polarization of generalized Nijenhuis torsions, Generalized Nijenhuis torsions and block-diagonalization of operator fields

Cites Work

• Haantjes structures for the Jacobi-Calogero model and the Benenti systems
• Recursion operators and Frobenius manifolds
• Haantjes manifolds and Veselov systems
• Reduction of Poisson manifolds
• Separation of variables for bi-Hamiltonian systems
• Bi-Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation variables
• Reduction of bi-Hamiltonian systems and separation of variables: An example from the Boussinesq hierarchy
• Haantjes algebras of the Lagrange top
• On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian.
• Bihamiltonian structures and Stäckel separability
• Haantjes algebras and diagonalization
• Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry
• Separability and symmetry operators for Painlevé metrics and their conformal deformations
• Beyond recursion operators
• Nilpotent integrability, reduction of dynamical systems and a third-order Calogero-Moser system
• Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor
• Special symmetric two-tensors, equivalent dynamical systems, cofactor and bi-cofactor systems
• Andrew Lenard: a mystery unraveled
• Block-separation of variables: a form of partial separation for natural Hamiltonians
• Lenard chains for classical integrable systems
• Separation of variables in multi-Hamiltonian systems: an application to the Lagrange top
• Classical and quantum superintegrability with applications
• A nonseparable quantum superintegrable system in 2D real Euclidean space
• On the integrability of stationary and restricted flows of the KdV hierarchy
• Schouten tensor and bi-Hamiltonian systems of hydrodynamic type
• A simple model of the integrable Hamiltonian equation
• About the existence of recursion operators for completely integrable Hamiltonian systems near a Liouville torus
• Quasi-bi-Hamiltonian systems and separability
• Recursion operators: Meaning and existence for completely integrable systems
• The quasi-bi-Hamiltonian formulation of the Lagrange top
• General algebraic identities for the Nijenhuis and Haantjes tensors
• Integrable Hamiltonian hierarchies. Spectral and geometric methods
• Webs, Lenard schemes, and the local geometry of bi-Hamiltonian Toda and Lax structures
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