26 citations · 59 across the 13 of their papers we have counts for
14 papers
Universality classes, Thermodynamics of Group Entropies, and Black Holes
Henrik Jeldtoft Jensen, Petr Jizba, Piergiulio Tempesta
Conventional Boltzmann--Gibbs statistical mechanics successfully describes systems with weak to moderate correlations, in which the number of accessible configurations grows…
Group Entropies and Mirror Duality: A Class of Flexible Mirror Descent Updates for Machine Learning
Andrzej Cichocki, Piergiulio Tempesta
We introduce a comprehensive theoretical and algorithmic framework that bridges formal group theory and group entropies with modern machine learning, paving the way for an infinite…
Laurent Sequences, Extended Rota Algebras and Categorical Discretization of Dynamical Systems
Miguel A. Rodriguez, Piergiulio Tempesta
We introduce a novel integrability-preserving discretization for a broad class of differential equations with variable coefficients, encompassing both linear and nonlinear cases. T…
Stäckel and Eisenhart lifts, Haantjes geometry and Gravitation
Ondřej Kubů, Piergiulio Tempesta
We study lifts of integrable systems by means of generalized Stäckel geometry. To this end, we present the notion of Stäckel lift as a unified setting for the construction of new c…
Group structure as a foundation for entropies
Henrik Jeldtoft Jensen, Piergiulio Tempesta
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be…
A new discretization of the Euler equation via the finite operator theory
Miguel A. Rodríguez, Piergiulio Tempesta
We propose a novel discretization procedure for the classical Euler equation based on the theory of Galois differential algebras and the finite operator calculus developed by G.C.…
Jacobi-Haantjes manifolds, integrability and dissipative mechanical systems
Rafael Azuaje, Piergiulio Tempesta
The notion of Jacobi-Haantjes manifold, consisting of a Jacobi manifold endowed with an algebra of extended Haantjes operator fields, is proposed as a natural geometric framework w…
A Frobenius-type theory for discrete systems
Daniel Reyes, Miguel A. Rodríguez, Piergiulio Tempesta
We develop an approach analogous to classical Frobenius theory for the analysis of singularities of ODEs in the case of discrete dynamical systems. Our methodology is based on the…
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…
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.…
Complexity-based permutation entropies: from deterministic time series to white noise
J. M. Amigó, R. Dale, P. Tempesta
This is a paper in the intersection of time series analysis and complexity theory that presents new results on permutation complexity in general and permutation entropy in particul…
Symmetry reduction and superintegrable Hamiltonian systems
M. A. Rodriguez, P. Tempesta, P. Winternitz
We construct complete sets of invariant quantities that are integrals of motion for two Hamiltonian systems obtained through a reduction procedure, thus proving that these systems…
Weak Transversality and Partially Invariant Solutions
A. M. Grundland, P. Tempesta, P. Winternitz
New exact solutions are obtained for several nonlinear physical equations, namely the Navier-Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinea…
Quantum models related to fouled Hamiltonians of the harmonic oscillator
P. Tempesta, E. Alfinito, R. A. Leo +1
We study a pair of canonoid (fouled) Hamiltonians of the harmonic oscillator which provide, at the classical level, the same equation of motion as the conventional Hamiltonian. The…