Person: Tempesta, Piergiulio
Loading...
First Name
Piergiulio
Last Name
Tempesta
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Físicas
Department
Física Teórica
Area
Matemática Aplicada
Identifiers
6 results
Search Results
Now showing 1 - 6 of 6
Item Generalized Nijenhuis torsions and block-diagonalization of operator fields(Journal of nonlinear science, 2023) Reyes Nozaleda, Daniel; Tempesta, Piergiulio; Tondo, GiorgioThe 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. We prove a general result ensuring that, given a family of commuting operator fields whose generalized Nijenhuis torsion of level m vanishes, there exists a local chart where all operators can be simultaneously block-diagonalized. We also introduce the notion of generalized Haantjes algebra, consisting of operators with a vanishing higher-level torsion, as a new algebraic structure naturally generalizing standard Haantjes algebras.Item Haantjes algebras of classical integrable systems (May, 2021)(Correction)(Annali di matematica pura ed applicata, 2021) Tempesta, Piergiulio; Tondo, GiorgioItem Higher Haantjes brackets and integrability(Communications in mathematical physics, 2021) Tempesta, Piergiulio; Tondo, GiorgioWe propose a new, infinite class of brackets generalizing the Frolicher-Nijenhuis bracket. This class can be reduced to a family of generalized Nijenhuis torsions recently introduced. In particular, the Haantjes bracket, the first example of our construction, is relevant in the characterization of Haantjes moduli of operators. We also prove that the vanishing of a higher-level Nijenhuis torsion of an operator field is a sufficient condition for the integrability of its eigen-distributions. This result (which does not require any knowledge of the spectral properties of the operator) generalizes the celebrated Haantjes theorem. The same vanishing condition also guarantees that the operator can be written, in a local chart, in a block-diagonal form.Item Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry(Communications in nonlinear science and numerical simulation, 2022) Reyes Nozaleda, Daniel; Tempesta, Piergiulio; Tondo, GiorgioWe show that the theory of classical Hamiltonian systems admitting separating variables can be formulated in the context of (omega, H ) structures. They are symplectic manifolds en-dowed with a compatible Haantjes algebra H , namely an algebra of (1,1)tensor fields with vanishing Haantjes torsion. A special class of coordinates, called Darboux-Haantjes coor-dinates, will be constructed from the Haantjes algebras associated with a separable sys-tem. These coordinates enable the additive separation of variables of the corresponding Hamilton-Jacobi equation. We shall prove that a multiseparable system admits as many omega H structures as sepa-ration coordinate systems. In particular, we will show that a large class of multiseparable, superintegrable systems, including the Smorodinsky-Winternitz systems and some physi-cally relevant systems with three degrees of freedom, possesses multiple Haantjes struc-tures. (C) 2021 Published by Elsevier B.V.Item Haantjes algebras and diagonalization(Journal of geometry and physics, 2021) Tempesta, Piergiulio; Tondo, GiorgioWe 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. They are also required to satisfy suitable compatibility conditions. Haantjes algebras naturally generalize several known interesting geometric structures, arising in Riemannian geometry and in the theory of integrable systems. At the same time, as we will show, they play a crucial role in the theory of diagonalization of operators on differentiable manifolds. Assuming that the operators of a Haantjes algebra are semisimple and commute, we shall prove that there exists a set of local coordinates where all operators can be diagonalized simultaneously. Moreover, in the general, non-semisimple case, they acquire simultaneously, in a suitable local chart, a block-diagonal form. (C) 2020 Elsevier B.V. All rights reserved.Item Haantjes Structures for the Jacobi-Calogero Model and the Benenti Systems.(Symmetry integrability and geometry: methods and applications (SIGMA), 2016) Tondo, Giorgio; Tempesta, PiergiulioIn the context of the theory of symplectic-Haantjes manifolds, we construct the Haantjes structures of generalized Stackel systems and, as a particular case, of the quasi-bi-Hamiltonian systems. As an application, we recover the Haantjes manifolds for the rational Calogero model with three particles and for the Benenti systems.