21 citations · 122 across the 24 of their papers we have counts for
25 papers
Periodic Magnetic Geodesics with Every Low Energy: Existence and Localization
Valerio Assenza, Gabriele Benedetti, Leonardo Macarini
Let be a Riemannian manifold equipped with a non-identically zero magnetic field represented by a closed -form . We allow to be non-compact and do not assume that…
Symplectic capacities of disc cotangent bundles of flat tori
Gabriele Benedetti, Johanna Bimmermann, Kai Zehmisch
We show that on the unit disc cotangent bundle of flat Riemannian tori, all normalized capacities coincide with twice the systole. The same result holds for flat, reversible Finsle…
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.…
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…
Relative Hofer-Zehnder capacity and positive symplectic homology
Gabriele Benedetti, Jungsoo Kang
We study the relationship between a homological capacity for Liouville domains defined using positive symplectic homology and the existence of periodic o…
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 local systolic optimality of Zoll contact forms
Alberto Abbondandolo, Gabriele Benedetti
We prove a normal form for contact forms close to a Zoll one and deduce that Zoll contact forms on any closed manifold are local maximizers of the systolic ratio. Corollaries of th…
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…
On a local systolic inequality for odd-symplectic forms
Gabriele Benedetti, Jungsoo Kang
The aim of this paper is to formulate a local systolic inequality for odd-symplectic forms (also known as Hamiltonian structures) and to establish it in some basic cases. Let b…
A local contact systolic inequality in dimension three
Gabriele Benedetti, Jungsoo Kang
Let be a contact form on a connected closed three-manifold . The systolic ratio of is defined as , where $T…
Invariance of symplectic cohomology and twisted cotangent bundles over surfaces
Gabriele Benedetti, Alexander F. Ritter
We prove that symplectic cohomology for open convex symplectic manifolds is invariant when the symplectic form undergoes deformations which may be non-exact and non-compactly suppo…
A local systolic-diastolic inequality in contact and symplectic geometry
Gabriele Benedetti, Jungsoo Kang
Let be a connected closed three-manifold, and let be the order of the torsion subgroup of . For a contact form on , we denote by $\mathrm{Volume}…
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…
Infinitely many periodic orbits just above the Mañé critical value on the 2-sphere
Gabriele Benedetti, Marco Mazzucchelli
We introduce a new critical value for Tonelli Lagrangians on the tangent bundle of the 2-sphere without minimizing measures supported on a point. We show that $c_…
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…
Lecture notes on closed orbits for twisted autonomous Tonelli Lagrangian flows
Gabriele Benedetti
These notes were prepared in occasion of a mini-course given by the author at the "CIMPA Research School - Hamiltonian and Lagrangian Dynamics" (10-19 March 2015 - Salto, Uruguay).…
On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus
Luca Asselle, Gabriele Benedetti
Let be a Riemannian two-torus and let be an oscillating -form on . We show that for almost every small positive number the magnetic flow o…
Magnetic Katok Examples on the two-sphere
Gabriele Benedetti
We show that there exist non-exact magnetic flows on the two-sphere having an energy level whose double cover is strictly contactomorphic to an irrational ellipsoid in $\mathbb C^2…
On the existence of periodic orbits for magnetic systems on the two-sphere
Gabriele Benedetti, Kai Zehmisch
We prove that there exist periodic orbits on almost all compact regular energy levels of a Hamiltonian function defined on a twisted cotangent bundle over the two-sphere. As a coro…
The Lusternik-Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles
Luca Asselle, Gabriele Benedetti
Let be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian and a twisted symplectic form. In this…
Infinitely many periodic orbits in non-exact oscillating magnetic fields on surfaces with genus at least two for almost every low energy level
Luca Asselle, Gabriele Benedetti
In this paper we consider oscillating non-exact magnetic fields on surfaces with genus at least two and show that for almost every energy level below a certain value $τ_+^*(g,σ…