Davide Polimeni
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Davide Polimeni has a total of 6 co-authors. Here are the top co-authors by number of shared publications:
- Diego Berti
Dipartimento di Matematica “Giuseppe Peano”, Università degli Studi di Torino, Turin, Italy
3 shared publications - Susanna Terracini
Dipartimento di Matematica “Giuseppe Peano”, Università di Torino, Torino, Italy
3 shared publications - Gian Marco Canneori
Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy
1 shared publication - Irene De Blasi
University of Turin, Italy
1 shared publication - Margaux Introna
Department of Mathematics, University of Turin, Turin, Italy
1 shared publication - Roberto Ciccarelli
Department of Mathematics, University of Turin, Turin, Italy
1 shared publication
Latest Publications
- Open Access
- 4 August 2026
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 250 (5) , 75
On the Regularity of Solutions to the Hamilton–Jacobi Equations for the N-Body Problem
We prove that certain renormalized value functions associated with the d -dimensional ( $$d\geqq 2$$ ) N -body problem corresponding to different limiting shapes of expanding solutions, under the assumption that the center of mass is at the origin, are viscosity solutions of the associated Hamilton–Jacobi equation. We analyze their singularities, defined as the initial configurations for which the minimizer of the associated variational problem is not unique. Moreover, we estimate the size of the closure of the singular set by proving its $$\mathcal {H}^{d(N-1)-1}$$ -rectifiability, and we provide an upper bound on the Hausdorff dimension of the set of regular conjugate points.- 4 August 2026
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 250 (5) , 75
Open AccessOn the Regularity of Solutions to the Hamilton–Jacobi Equations for the N-Body Problem
We prove that certain renormalized value functions associated with the d -dimensional ( $$d\geqq 2$$ ) N -body problem corresponding to different limiting shapes of expanding solutions, under the assumption that the center of mass is at the origin, are viscosity solutions of the associated Hamilton–Jacobi equation. We analyze their singularities, defined as the initial configurations for which the minimizer of the associated variational problem is not unique. Moreover, we estimate the size of the closure of the singular set by proving its $$\mathcal {H}^{d(N-1)-1}$$ -rectifiability, and we provide an upper bound on the Hausdorff dimension of the set of regular conjugate points. - Open Access
Symmetric solutions of the $n$-body problem: a numerical study of Floquet multipliers and Morse indices
In this paper, we consider periodic solutions of the $n$-body problem that satisfy symmetry constraints, expressed through invariance under finite group actions. We focus on their stability properties and present algorithms specifically designed for the computation of Floquet multipliers and Morse indices. Numerical results are provided to illustrate our methods in both two and three dimensional configuration spaces, and for different choices on the number of bodies.
Open AccessSymmetric solutions of the $n$-body problem: a numerical study of Floquet multipliers and Morse indices
In this paper, we consider periodic solutions of the $n$-body problem that satisfy symmetry constraints, expressed through invariance under finite group actions. We focus on their stability properties and present algorithms specifically designed for the computation of Floquet multipliers and Morse indices. Numerical results are provided to illustrate our methods in both two and three dimensional configuration spaces, and for different choices on the number of bodies.
- Open Access
On the regularity of solutions to the Hamilton-Jacobi equations for the N-body problem
We prove that certain suitably renormalized value functions associated with the $d$-dimensional ($d\geq2$) $N$-body problem corresponding to different limiting shapes of expanding solutions, under the assumption that the center of mass is at the origin, are viscosity solutions of the associated Hamilton-Jacobi equation. We analyze their singularities, defined as the initial configurations for which the minimizer of the associated variational problem is not unique. Moreover, we estimate the size of the closure of the singular set by proving its $\mathcal{H}^{d(N-1)-1}$-rectifiability, and we provide an upper bound on the Hausdorff dimension of the set of regular conjugate points.
Open AccessOn the regularity of solutions to the Hamilton-Jacobi equations for the N-body problem
We prove that certain suitably renormalized value functions associated with the $d$-dimensional ($d\geq2$) $N$-body problem corresponding to different limiting shapes of expanding solutions, under the assumption that the center of mass is at the origin, are viscosity solutions of the associated Hamilton-Jacobi equation. We analyze their singularities, defined as the initial configurations for which the minimizer of the associated variational problem is not unique. Moreover, we estimate the size of the closure of the singular set by proving its $\mathcal{H}^{d(N-1)-1}$-rectifiability, and we provide an upper bound on the Hausdorff dimension of the set of regular conjugate points.
- Open Access
- 12 September 2024
- Published by Springer Nature in Inventiones Mathematicae
- Vol. 238 (2) , 585-635
On the existence of minimal expansive solutions to the $N$-body problem
We deal, for the classical $N$ N -body problem, with the existence of action minimizing half entire expansive solutions with prescribed asymptotic direction and initial configuration of the bodies. We tackle the cases of hyperbolic, hyperbolic-parabolic and parabolic arcs in a unified manner. Our approach is based on the minimization of a renormalized Lagrangian action on a suitable functional space. With this new strategy, we are able to confirm the already-known results of the existence of both hyperbolic and parabolic solutions, and we prove for the first time the existence of hyperbolic-parabolic solutions for any prescribed asymptotic expansion in a suitable class. Associated with each element of this class we find a viscosity solution of the Hamilton-Jacobi equation as a linear correction of the value function. Besides, we also manage to give a precise description of the growth of parabolic and hyperbolic-parabolic solutions.
- 12 September 2024
- Published by Springer Nature in Inventiones Mathematicae
- Vol. 238 (2) , 585-635
Open AccessOn the existence of minimal expansive solutions to the $N$-body problem
We deal, for the classical $N$ N -body problem, with the existence of action minimizing half entire expansive solutions with prescribed asymptotic direction and initial configuration of the bodies. We tackle the cases of hyperbolic, hyperbolic-parabolic and parabolic arcs in a unified manner. Our approach is based on the minimization of a renormalized Lagrangian action on a suitable functional space. With this new strategy, we are able to confirm the already-known results of the existence of both hyperbolic and parabolic solutions, and we prove for the first time the existence of hyperbolic-parabolic solutions for any prescribed asymptotic expansion in a suitable class. Associated with each element of this class we find a viscosity solution of the Hamilton-Jacobi equation as a linear correction of the value function. Besides, we also manage to give a precise description of the growth of parabolic and hyperbolic-parabolic solutions.