Beyond recursion operators

2017/12/24 by Kosmann-Schwarzbach, Yvette · 1 citation
#01A60 #17B70 #37J99 #70G45 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #History and Overview (math.HO) #Primary 58-03 #Secondary 53D45

paper · doi:10.48550/arxiv.1712.08908

Abstract

We briefly recall the history of the Nijenhuis torsion of (1,1)-tensors on manifolds and of the lesser-known Haantjes torsion. We then show how the Haantjes manifolds of Magri and the symplectic-Haantjes structures of Tempesta and Tondo generalize the classical approach to integrable systems in the bi-hamiltonian and symplectic-Nijenhuis formalisms, the sequence of powers of the recursion operator being replaced by a family of commuting Haantjes operators.

Cited by

• Banach Poisson-Lie groups, Lax equations and the AKS theorem in infinite dimensions

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