83 citations · 322 across the 19 of their papers we have counts for
19 papers
Hamiltonian integrable systems in a magnetic field and Symplectic-Haantjes geometry
Ondřej Kubů, Daniel Reyes, Piergiulio Tempesta +1
We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional Riemannian configuration spaces. We prove that these systems admit no…
Partial separability and symplectic-Haantjes manifolds
Daniel Reyes, Piergiulio Tempesta, Giorgio Tondo
A theory of partial separability for classical Hamiltonian systems is proposed in the context of Haantjes geometry. As a general result, we show that the knowledge of a non-semisim…
Polarization of generalized Nijenhuis torsions
Piergiulio Tempesta, Giorgio Tondo
In this work, we introduce the notion of polarization of generalized Nijenhuis torsions and establish several algebraic identities. We prove that these polarizations are relevant i…
Generalized Nijenhuis Torsions and block-diagonalization of operator fields
Daniel Reyes Nozaleda, Piergiulio Tempesta, Giorgio Tondo
The theory of generalized Nijenhuis torsions, which extends the classical notions due to Nijenhuis and Haantjes, offers new tools for the study of normal forms of operator fields.…
Classical Multiseparable Hamiltonian Systems, Superintegrability and Haantjes Geometry
Daniel Reyes Nozaleda, Piergiulio Tempesta, Giorgio Tondo
We show that the theory of classical Hamiltonian systems admitting separating variables can be formulated in the context of () structures. They are symplectic manif…
Higher Haantjes Brackets and Integrability
Piergiulio Tempesta, Giorgio Tondo
We propose a new, infinite class of brackets generalizing the Frölicher--Nijenhuis bracket. This class can be reduced to a family of generalized Nijenhuis torsions recently introdu…
Haantjes Algebras of the Lagrange Top
Giorgio Tondo
A symplectic-Haantjes manifold and a Poisson-Haantjes manifold for the Lagrange top are studied and a set of Darboux-Haantjes coordinates are computed. Such coordinates are separat…
Haantjes Algebras and Diagonalization
Piergiulio Tempesta, Giorgio Tondo
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.…
Haantjes Structures for the Jacobi-Calogero Model and the Benenti Systems
Giorgio Tondo, Piergiulio Tempesta
In the context of the theory of symplectic-Haantjes manifolds, we construct the Haantjes structures of generalized Stäckel systems and, as a particular case, of the quasi-bi-Hamilt…
On the characterization of integrable systems via the Haantjes geometry
Piergiulio Tempesta, Giorgio Tondo
We prove that the existence of a Haantjes structure is a necessary and sufficient condition for a Hamiltonian system to be integrable in the Liouville-Arnold sense. This structure,…
Haantjes Algebras of Classical Integrable Systems
Piergiulio Tempesta, Giorgio Tondo
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…
Generalized Lenard Chains, Separation of Variables and Superintegrability
Piergiulio Tempesta, Giorgio Tondo
We show that the notion of generalized Lenard chains naturally allows formulation of the theory of multi-separable and superintegrable systems in the context of bi-Hamiltonian geom…
Separation of variables in multi-Hamiltonian systems: an application to the Lagrange top
C. Morosi, G. Tondo
Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the reduction of the vector field and of the Poisson tensors. We show…
The quasi-bi-Hamiltonian formulation of the Lagrange top
C. Morosi, G. Tondo
Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and…
Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchy
G. Falqui, F. Magri, G. Tondo
We discuss the Boussinesq system with stationary, within a general framework for the analysis of stationary flows of n-Gel'fand-Dickey hierarchies. We show how a careful use…
Bi-Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation variables
G. Tondo, C. Morosi
We discuss from a bi-Hamiltonian point of view the Hamilton-Jacobi separability of a few dynamical systems. They are shown to admit, in their natural phase space, a quasi-bi-Hamilt…
On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian
C. Morosi, G. Tondo
It is shown that a class of dynamical systems (encompassing the one recently considered by F. Calogero [J. Math. Phys. 37 (1996) 1735]) is both quasi-bi-Hamiltonian and bi-Hamilton…
Quasi-BiHamiltonian Systems and Separability
C. Morosi, G. Tondo
Two quasi--biHamiltonian systems with three and four degrees of freedom are presented. These systems are shown to be separable in terms of Nijenhuis coordinates. Moreover the most…
On the integrability of stationary and restricted flows of the KdV hierarchy.
G. Tondo
A bi--Hamiltonian formulation for stationary flows of the KdV hierarchy is derived in an extended phase space. A map between stationary flows and restricted flows is constructed: i…