Eugenio Pozzoli

activity

20232026

collaborators

11 papers

math.DG2026

The Lie algebra generated by gradient vector fields

Bettina Kazandjian, Omar Mohsen, Eugenio Pozzoli

Let $M$ be a smooth compact manifold, and $g$ a smooth non-degenerate symmetric bilinear form on $T M$ . We prove that every smooth vector field can be written as a finite linear com…

math.AP2026

Approximate controllability in small times of bilinear Schr{ö}dinger equations with magnetic drift

Eugenio Pozzoli

We study the small-time approximate controllability of bilinear Schr{ö}dinger equations, where the drift is a magnetic Schr{ö}dinger operator and the control is an electric potenti…

math.OC2026

Approximate controllability of a bilinear wave equation and minimum time

Karine Beauchard, Thomas Perrin, Eugenio Pozzoli

We study the global approximate controllability (GAC) of a Klein-Gordon wave equation, posed on the torus $T^{d}$ of arbitrary dimension $d \in N^{*}$ , with bilinear c…

math.AP2025

Small-time approximate controllability of the logarithmic Schr\''dinger equation

Karine Beauchard, Rémi Carles, Eugenio Pozzoli

We consider Schr{ö}dinger equations with logarithmic nonlinearity and bilinear controls, posed on $T^{d}$ or $R^{d}$ . We prove their small-time global $L^{2}$ -approxima…

math.SG2025

Orbits and attainable Hamiltonian diffeomorphisms of mechanical Liouville equations

Bettina Kazandjian, Eugenio Pozzoli, Mario Sigalotti

We study the approximate controllability problem for Liouville transport equations along a mechanical Hamiltonian vector field. Such PDEs evolve inside the orbit $$\mathcal{O}(ρ_0)…

math.OC2025

Good Lie Brackets for classical and quantum harmonic oscillators

Andrei Agrachev, Bettina Kazandjian, Eugenio Pozzoli

We study the small-time controllability problem on the Lie groups $S L_{2} (R)$ and $S L_{2} (R) ⋉ H_{d} (R)$ with Lie bracket methods (here $H_{d}(\mathbb{R…

math.OC2025

Approximation of diffeomorphisms for quantum state transfers

Eugenio Pozzoli, Alessandro Scagliotti

In this paper, we seek to combine two emerging standpoints in control theory. On the one hand, recent advances in infinite-dimensional geometric control have unlocked a method for…

math.OC2024

Small-time approximate controllability of bilinear Schrödinger equations and diffeomorphisms

Karine Beauchard, Eugenio Pozzoli

We consider Schrödinger PDEs, posed on a boundaryless Riemannian manifold $M$ , with bilinear control. We propose a new method to prove the global $L^{2}$ -approximate controllability.…

math.AP2024

On the small-time bilinear control of a nonlinear heat equation: global approximate controllability and exact controllability to trajectories

Alessandro Duca, Eugenio Pozzoli, Cristina Urbani

In this work we analyse the small-time reachability properties of a nonlinear parabolic equation, by means of a bilinear control, posed on a torus of arbitrary dimension $d$ . Under…

math.OC2024

Examples of small-time controllable Schrödinger equations

Karine Beauchard, Eugenio Pozzoli

A variety of physically relevant bilinear Schrödinger equations are known to be approximately controllable in large times. There are however examples which are approximately contro…

math.OC2023

Small-time controllability for the nonlinear Schrödinger equation on $R^{N}$ via bilinear electromagnetic fields

Alessandro Duca, Eugenio Pozzoli

We address the small-time controllability problem for a nonlinear Schrödinger equation (NLS) on $R^{N}$ in the presence of magnetic and electric external fields. We choose a…