The bi-Hamiltonian structure is established for the perturbation equations of the KdV
hierarchy and the perturbation equations themselves also provide examples among typical …

This is both a textbook and a monograph. It is partially based on a two-semester course,
held by the author for third-year students in physics and mathematics at the University of …

The problem of whether or not the equations of motion of a quantum system determine the
commutation relations was posed by EP Wigner in 1950. A similar problem (known as “The …

A tensorial approach to the theory of classical Hamiltonian integrable systems is proposed,
based on the geometry of Haantjes tensors. We introduce the class of symplectic-Haantjes …

Integrals of motion are constructed from noncommutative (NC) Kepler dynamics,
generating,, and dynamical symmetry groups. The Hamiltonian vector field is derived in …

This paper develops a new theory of tensor invariants of a completely integrable non-
degenerate Hamiltonian system on a smooth manifold M n. The central objects in this theory …

We introduce the notion of Haantjes algebra: It consists of an assignment of a family of
operator fields on a differentiable manifold, each of them with vanishing Haantjes torsion …

We briefly review the most relevant aspects of complete integrability for classical systems
and identify those aspects which should be present in a definition of quantum integrability …

A recursion operator for a geodesic flow, in a noncommutative (NC) phase space endowed
with a Minkowski metric, is constructed and discussed in this work. A NC Hamiltonian …

Recursion Operators: Meaning and Existence for Completely Integrable Systems Page 1 ESI
The Erwin Schrödinger International Boltzmanngasse 9 Institute for Mathematical Physics …