Abstract
We study orbits and reachable sets of generic couples of Hamiltonians H 1, H 2 on a symplectic manifold N. We prove that, C k -generically for k large enough, orbits coincide with the whole of N and that the same is true for reachable sets when N is compact. Our results are stated in terms of a strong form of genericity which makes use of the notion of rectifiable subsets of positive codimension in Banach or Frechet spaces.
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