5 papers
Density of fibers for the filtered Fukaya category of
Stéphane Guillermou, Claude Viterbo, Bingyu Zhang
We answer a question of Biran and Cornea about the density of iterated cones of fibers in the Fukaya category of a cotangent bundle. We prove that indeed if we take a dense set of…
Higher Dimensional Birkhoff attractors (with an appendix by Maxime Zavidovique)
Marie-Claude Arnaud, Vincent Humilière, Claude Viterbo
We extend to higher dimensions the notion of Birkhoff attractor of a dissipative map. We prove that this notion coincides with the classical Birkhoff attractor. We prove that for t…
On the supports in the Humilière completion and -coisotropic sets
Claude Viterbo
The symplectic spectral metric on the set of Lagrangian submanifolds or Hamiltonian maps can be used to define a completion of these spaces. For an element of such a completion, we…
Non-convex Mather's theory and the Conley conjecture on the cotangent bundle of the torus
Claude Viterbo
The aim of this paper is to use the methods and results of symplectic homogenization (see [V4]) to prove existence of periodic orbits and invariant measures with rotation number de…
Regular Lagrangians are smooth Lagrangians
Tomohiro Asano, Stéphane Guillermou, Yuichi Ike +1
We prove that for any element in the -completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle, if its -support is a smooth Lagrangian…