Person: Tempesta, Piergiulio
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First Name
Piergiulio
Last Name
Tempesta
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Físicas
Department
Física Teórica
Area
Matemática Aplicada
Identifiers
13 results
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Now showing 1 - 10 of 13
Item On higher-dimensional superintegrable systems: a new family of classical and quantum Hamiltonian models(Journal of physics A: Mathematical and theoretical, 2022) Rodríguez González, Miguel Ángel; Tempesta, PiergiulioWe introduce a family of n-dimensional Hamiltonian systems which, contain, as special reductions, several superintegrable systems as the Tremblay-Turbiner-Winternitz system, a generalized Kepler potential and the anisotropic harmonic oscillator with Rosochatius terms. We conjecture that there exist special values in the space of parameters, apart from those leading to known cases, for which this new Hamiltonian family is superintegrable.Item Manual de Álgebra(2021) Tempesta, PiergiulioItem 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 Permutation group entropy: a new route to complexity for real-valued processes(Chaos, 2022) Amigó, José M.; Dale, Roberto; Tempesta, PiergiulioThis is a review of group entropy and its application to permutation complexity. Specifically, we revisit a new approach to the notion of complexity in the time series analysis based on both permutation entropy and group entropy. As a result, the permutation entropy rate can be extended from deterministic dynamics to random processes. More generally, our approach provides a unified framework to discuss chaotic and random behaviors.Item Universality classes and information-theoretic measures of complexity via group entropies.(Scientific reports, 2020) Tempesta, Piergiulio; Jensen, Henrik JeldtoftWe introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series of natural axioms. In addition, we require extensivity in order to ensure that our information measures are meaningful. The entropic measures proposed are suitably defined for describing universality classes of complex systems, each characterized by a specific state space growth rate function.Item Information geometry, complexity measures and data analysis(Entropy, 2022) Amigó, José M.; Tempesta, PiergiulioItem 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.