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An involutivity theorem for a class of Poisson quasi-Nijenhuis manifolds
Eber Chuño Vizarreta, Gregorio Falqui, Igor Mencattini +1
This note aims to continue our study about the applications of Poisson quasi-Nijenhuis geometry to the theory of classical completely integrable systems. More precisely, we will pr…
Poisson quasi-Nijenhuis manifolds, closed Toda lattices, and generalized recursion relations
Eber Chuño Vizarreta, Gregorio Falqui, Igor Mencattini +1
We present two involutivity theorems in the context of Poisson quasi-Nijenhuis %(PqN) manifolds. The second one stems from recursion relations that generalize the so called Lenard-…
What is the Magnus Expansion?
Kurusch Ebrahimi-Fard, Igor Mencattini, Alexandre Quesney
The Magnus expansion, introduced by Wilhelm Magnus in 1954, is an infinite Lie series employed to express solutions for first-order homogeneous linear differential equations involv…
Poisson quasi-Nijenhuis deformations of the canonical PN structure
Gregorio Falqui, Igor Mencattini, Marco Pedroni
We present a result which allows us to deform a Poisson-Nijenhuis manifold into a Poisson quasi-Nijenhuis manifold by means of a closed 2-form. Under an additional assumption, the…
Poisson quasi-Nijenhuis manifolds and the Toda system
G. Falqui, I. Mencattini, G. Ortenzi +1
The notion of Poisson quasi-Nijenhuis manifold generalizes that of Poisson-Nijenhuis manifold. The relevance of the latter in the theory of completely integrable systems is well es…
Bi-Hamiltonian geometry and canonical spectral coordinates for the Rational Calogero-Moser system
Gregorio Falqui, Igor Mencattini
We reconsider the (rational) Calogero-Moser system from the point of view of bi-Hamiltonian geometry. By using geometrical tools of the latter, we explicitly construct set(s) of sp…