On some completions of the space of Hamiltonian maps

Details On some completions of the space of Hamiltonian maps On some completions of the space of Hamiltonian maps

2005-11-16

arxiv.org/abs/math/0511418v3

Mathematics

Symplectic Geometry

31 pages

Scientific paper

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.

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