Marco Mazzucchelli

On Tonelli periodic orbits with low energy on surfaces

We prove that, on a closed surface, a Lagrangian system defined by a Tonelli Lagrangian

Symplectically degenerate maxima via generating functions

L

The Multiplicity Problem for Periodic Orbits of Magnetic Flows on the 2-Sphere

possesses a periodic orbit that is a local minimizer of the free-period action functional on every energy level belonging to the low range of energies

Isometry-invariant geodesics and the fundamental group

(e_0(L),c_{\mathrm{u}}(L))

Isometry-invariant geodesics and the fundamental group, II

. We also prove that almost every energy level in

On the multiplicity of isometry-invariant geodesics on product manifolds

(e_0(L),c_{\mathrm{u}}(L))

Marked boundary rigidity for surfaces

possesses infinitely many periodic orbits. These statements extend two results, respectively due to Taimanov and Abbondandolo-Macarini-Mazzucchelli-Paternain, valid for the special case of electromagnetic Lagrangians.

On the existence of infinitely many closed geodesics on non-compact manifolds

We provide a simple proof of a theorem due to Nancy Hingston, asserting that symplectically degenerate maxima of any Hamiltonian diffeomorphism

A characterization of Zoll Riemannian metrics on the 2-sphere: A CHARACTERIZATION OF ZOLL RIEMANNIAN METRICS ON THE 2-SPHERE

\phi