4 citations · 4 across the 9 of their papers we have counts for
10 papers
Remarks on periodic points, flux, and the mean index in symplectic dynamics
Marcelo S. Atallah, Marta Batoréo, Brayan Ferreira
It is shown that a symplectic isotopy with non-degenerate end-point on a closed symplectically Calabi--Yau manifold has simple periodic points of arbitrarily large period under a s…
On the spectral diameter of the Grassmannians
Habib Alizadeh, Marcelo S. Atallah, Dylan Cant +1
The diameter of the spectral pseudometric on the universal cover of the Hamiltonian diffeomorphism group of is shown to be finite whenever is a prime number.…
-rigidity of the Hamiltonian diffeomorphism group of symplectic rational surfaces
Marcelo Atallah, Cheuk Yu Mak, Weiwei Wu
We investigate the -topology of the group of symplectic diffeomorphisms of positive symplectic rational surfaces. For all but a few exceptions, we prove that the group of Hami…
Weinstein exactness of nearby Lagrangians and related questions
Marcelo S. Atallah, Jean-Philippe Chassé, Rémi Leclercq +1
We address the following problem: if a Hamiltonian diffeomorphism maps a Lagrangian submanifold to a small Weinstein neighborhood of , is the image necessarily Hamiltonian i…
The number of periodic points of surface symplectic diffeomorphisms
Marcelo S. Atallah, Marta Batoréo, Brayan Ferreira
We use symplectic tools to establish a smooth variant of Franks theorem for a closed orientable surface of positive genus ; it implies that a symplectic diffeomorphism isotopic…
The spectral diameter of a symplectic ellipsoid
Habib Alizadeh, Marcelo S. Atallah, Dylan Cant
The spectral diameter of a symplectic ball is shown to be equal to its capacity; this result upgrades the known bound by a factor of two and yields a simple formula for the spectra…
Lagrangian Intersections and the spectral norm in convex-at-infinity symplectic manifolds
Habib Alizadeh, Marcelo S. Atallah, Dylan Cant
Given a compact Lagrangian in a semipositive convex-at-infinity symplectic manifold , we establish a cup-length estimate for the action values of associated to a Hamilto…
On the Hofer-Zehnder conjecture for semipositive symplectic manifolds
Marcelo S. Atallah, Han Lou
We show that, on a closed semipositive symplectic manifold with semisimple quantum homology, any Hamiltonian diffeomorphism possessing more contractible fixed points, counted homol…
Remarks on symplectic circle actions, torsion and loops
Marcelo S. Atallah
We study loops of symplectic diffeomorphisms of closed symplectic manifolds. Our main result, which is valid for a large class of symplectic manifolds, shows that the flux of a sym…
Hamiltonian no-torsion
Marcelo S. Atallah, Egor Shelukhin
In 2002 Polterovich has notably established that on closed aspherical symplectic manifolds, Hamiltonian diffeomorphisms of finite order, which we call Hamiltonian torsion, must in…