11 citations · 22 across the 6 of their papers we have counts for
11 papers
Lorentz-Finsler metrics on symplectic and contact transformation groups
Alberto Abbondandolo, Gabriele Benedetti, Leonid Polterovich
In these notes we discuss Lorentz-Finsler metrics, a notion originated in relativity theory, on certain groups of symplectic and contact transformations. Some basic geometric quest…
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…
First steps into the world of systolic inequalities: From Riemannian to symplectic geometry
Gabriele Benedetti
Our aim is to give a friendly introduction for students to systolic inequalities. We will stress the relationships between the classical formulation for Riemannian metrics and more…
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…
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 a systolic inequality for closed magnetic geodesics on surfaces
Gabriele Benedetti, Jungsoo Kang
We apply a local systolic-diastolic inequality for contact forms and odd-symplectic forms on three-manifolds to bound the magnetic length of closed curves with prescribed geodesic…