21 citations · 88 across the 25 of their papers we have counts for
5 papers · 1 filter
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…