On the stability of Ma\~n\'e critical hypersurfaces (2009)
Macarini, Leonardo, Paternain, Gabriel P.
We construct examples of Tonelli Hamiltonians on $\T^n$ (for any $n\geq 2$) such that the hypersurfaces corresponding to the Ma\~n\'e critical value are stable (i.e. geodesible). We also provide a...
Periodic orbits for exact magnetic flows on surfaces (2004)
Contreras, Gonzalo, Macarini, Leonardo, Paternain, Gabriel P.
We show that any exact magnetic flow on a closed surface has periodic orbits in all energy levels. Moreover, we give homological and homotopical properties of these periodic orbits in terms of the...
Hofer-Zehnder capacity of standard cotangent bundles (2003)
Let $M$ be a compact manifold with an effective semi-free circle action whose fixed point set has trivial normal bundle. We prove that its cotangent bundle endowed with the canonical symplectic form...
Macarini, Leonardo, Schlenk, Felix
The Hofer-Zehnder theorem states that almost every hypersurface in a thickening of a hypersurface $S$ in a symplectic manifold $(M,\omega)$ carries a closed characteristic provided that $S$ bounds a...
Symplectic manifolds with disconnected contact type boundary in dimension 4n (2003)
We give examples of compact symplectic manifolds with disconnected contact type boundary in dimension $4n$ for any $n\geq 1$. The example is given by a subset of the tangent bundle of a compact...
Hofer-Zehnder semicapacity of cotangent bundles and symplectic submanifolds (2003)
We introduce the concept of Hofer-Zehnder $G$-semicapacity (or $G$-sensitive Hofer-Zehnder capacity) and prove that given a geometrically bounded symplectic manifold $(M,\omega)$ and an open subset...
Hofer-Zehnder capacity and Hamiltonian circle actions (2002)
We introduce the Hofer-Zehnder $G$-semicapacity $c_{HZ}^G(M,\om)$ of a symplectic manifold $(M,\om)$ with respect to a subgroup $G \subset \pi_1(M)$ ($c_{HZ}(M,\om) \leq c^G_{HZ}(M,\om)$) and prove...