On some completions of the space of Hamiltonian maps
Symplectic Geometry
2013-06-27 v3 Analysis of PDEs
Abstract
We study the completions of the space of Hamiltonian diffeomorphisms of the standard linear symplectic space, for Viterbo's distance and some others derived from it, we study their different inclusions and give some of their properties. In particular, we give a convergence criterion for these distances. This allows us to prove that the completions contain non-ordinary elements, as for example, discontinuous Hamiltonians. We also prove that some dynamical properties of Hamiltonian systems are preserved in the completions.
Keywords
Cite
@article{arxiv.math/0511418,
title = {On some completions of the space of Hamiltonian maps},
author = {Vincent Humilière},
journal= {arXiv preprint arXiv:math/0511418},
year = {2013}
}
Comments
31 pages