21 citations · 88 across the 25 of their papers we have counts for
29 papers
Relative equilibria, linear stability and electromagnetic curvature
Luca Asselle, Giorgia Testolina
In this paper we study the linear stability of relative equilibria in the Newtonian -body problem from the viewpoint of electromagnetic systems. We first examine the effect of t…
Morse homology for strongly indefinite functionals on Banach spaces
L. Asselle, S. Cingolani, M. Starostka
In this paper we lay the foundations for the Morse theoretical study of strongly indefinite functionals on Banach manifolds by developing the local theory for a specific model clas…
On the Zoll deformations of the Kepler problem
Asselle Luca, Baranzini Stefano
A celebrated result of Bertrand states that the only central force potentials on the plane with the property that all bounded orbits are periodic are the Kepler potential and the p…
A note on the Morse homology for a class of functionals in Banach spaces involving the -Laplacian
L. Asselle, M. Starostka
In this paper we show how to construct Morse homology for an explicit class of functionals involving the -Laplacian. The natural domain of definition of such functionals is the…
Non-minimality and instability of brake orbits for natural Lagrangians on Riemannian manifolds
Luca Asselle, Xijun Hu, Alessandro Portaluri +1
We investigate minimality and stability of periodic brake orbits in natural Lagrangian systems on smooth Riemannian manifolds. We prove that every non-constant periodic brake orbit…
Zoll magnetic systems on the two-torus: a Nash-Moser construction
Luca Asselle, Gabriele Benedetti, Massimiliano Berti
We construct an infinite-dimensional family of smooth integrable magnetic systems on the two-torus which are Zoll, meaning that all the unit-speed magnetic geodesics are periodic.…
The Arnold conjecture in and the Conley index
L. Asselle, M. Izydorek, M. Starostka
In this paper we give an alternative, purely Conley index based proof of the Arnold conjecture in asserting that a Hamiltonian diffeomorphism of $\mathbb C\m…
Spectral stability, spectral flow and circular relative equilibria for the Newtonian -body problem
Luca Asselle, Alessandro Portaluri, Li Wu
For the Newtonian (gravitational) -body problem in the Euclidean -dimensional space, , the simplest possible periodic solutions are provided by circular relative equi…
Non-resonant circles for strong magnetic fields on surfaces
L. Asselle, G. Benedetti
We study non-resonant circles for strong magnetic fields on a closed, connected, oriented surface and show how these can be used to prove the existence of trapping regions and of p…
Bifurcations of balanced configurations for the Newtonian -body problem in
Luca Asselle, Marco Fenucci, Alessandro Portaluri
For the gravitational -body problem, the simplest motions are provided by those rigid motions in which each body moves along a Keplerian orbit and the shape of the system is a c…
Morse theory for -balanced configurations in the Newtonian -body problem
Luca Asselle, Alessandro Portaluri
For the Newtonian (gravitational) -body problem in the Euclidean -dimensional space, the simplest possible solutions are provided by those rigid motions (homographic solution…
The Palais-Smale condition for the Hamiltonian action on a mixed regularity space of loops in cotangent bundles and applications
Luca Asselle, Maciej Starostka
We show that the Hamiltonian action satisfies the Palais-Smale condition over a "mixed regularity" space of loops in cotangent bundles, namely the space of loops with regularity $H…
Normal forms for strong magnetic systems on surfaces: Trapping regions and rigidity of Zoll systems
Luca Asselle, Gabriele Benedetti
We prove a normal form for strong magnetic fields on a closed, oriented surface and use it to derive two dynamical results for the associated flow. First, we show the existence of…
On the rigidity of Zoll magnetic systems on surfaces
Luca Asselle, Christian Lange
In this paper we study rigidity aspects of Zoll magnetic systems on closed surfaces. We characterize magnetic systems on surfaces of positive genus given by constant curvature metr…
Waist theorems for Tonelli systems in higher dimensions
Luca Asselle, Marco Mazzucchelli
We study the periodic orbits problem on energy levels of Tonelli Lagrangian systems over configuration spaces of arbitrary dimension. We show that, when the fundamental group is fi…
Integrable magnetic flows on the two-torus: Zoll examples and systolic inequalities
Luca Asselle, Gabriele Benedetti
In this paper we study some aspects of integrable magnetic systems on the two-torus. On the one hand, we construct the first non-trivial examples with the property that all magneti…
On geodesic flows with symmetries and closed magnetic geodesics on orbifolds
Luca Asselle, Felix Schmäschke
Let be a closed manifold admitting a locally-free action of a compact Lie group . In this paper we study the properties of geodesic flows on given by Riemannian metrics…
Closed geodesics with local homology in maximal degree on non-compact manifolds
Luca Asselle, Marco Mazzucchelli
We show that, on a complete and possibly non-compact Riemannian manifold of dimension at least 2 without close conjugate points at infinity, the existence of a closed geodesic with…
Minimal boundaries in Tonelli Lagrangian systems
Luca Asselle, Gabriele Benedetti, Marco Mazzucchelli
We prove several new results concerning action minimizing periodic orbits of Tonelli Lagrangian systems on an oriented closed surface . More specifically, we show that for every…
The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere
Alberto Abbondandolo, Luca Asselle, Gabriele Benedetti +2
We consider magnetic Tonelli Hamiltonian systems on the cotangent bundle of the 2-sphere, where the magnetic form is not necessarily exact. It is known that, on very low and on hig…
On the existence of closed magnetic geodesics via symplectic reduction
Luca Asselle, Felix Schmäschke
Let be a closed Riemannian manifold and be a closed 2-form on representing an integer cohomology class. In this paper, using symplectic reduction, we show how the p…
Smooth Hamilton-Jacobi solutions for the Horocycle flow
Luca Asselle
In this paper we compute all the smooth solutions to the Hamilton-Jacobi equation associated with the horocycle flow. This can be seen as the Euler-Lagrange flow (restricted to the…
On the existence of infinitely many closed geodesics on non-compact manifolds
Luca Asselle, Marco Mazzucchelli
We prove that any complete (and possibly non-compact) Riemannian manifold possesses infinitely many closed geodesics provided its free loop space has unbounded Betti numbers in…
On Tonelli periodic orbits with low energy on surfaces
Luca Asselle, Marco Mazzucchelli
We prove that, on a closed surface, a Lagrangian system defined by a Tonelli Lagrangian possesses a periodic orbit that is a local minimizer of the free-period action functiona…