33 citations · 144 across the 22 of their papers we have counts for
33 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…
Multiplicity of closed Reeb orbits on contact manifolds with periodic equivariant symplectic homology
Miguel Abreu, Leonardo Macarini
We consider closed contact manifolds with periodic positive equivariant symplectic homology. This is a very large class of contact manifolds and, to the best of our knowled…
Contact flexibility and rigidity for toric Gorenstein prequantizations and Ehrhart theory of toric diagrams
Miguel Abreu, Leonardo Macarini, António Rocha-Neves
Gorenstein toric contact manifolds are good toric contact manifolds with zero first Chern class that are completely determined by certain integral convex polytopes called toric dia…
Periodic orbits of non-degenerate lacunary contact forms on prequantization bundles
Miguel Abreu, Leonardo Macarini
A non-degenerate contact form is lacunary if the indexes of every contractible periodic Reeb orbit have the same parity. To the best of our knowledge, every contact form with finit…
Symmetric periodic Reeb orbits on the sphere
Miguel Abreu, Hui Liu, Leonardo Macarini
A long standing conjecture in Hamiltonian Dynamics states that every contact form on the standard contact sphere has at least simple periodic Reeb orbits. In this…
Contact invariants of Q-Gorenstein toric contact manifolds, the Ehrhart polynomial and Chen-Ruan cohomology
Miguel Abreu, Leonardo Macarini, Miguel Moreira
Q-Gorenstein toric contact manifolds provide an interesting class of examples of contact manifolds with torsion first Chern class. They are completely determined by certain rationa…