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Generic transitivity for couples of Hamiltonians

Mandorino, Vito (2013), Generic transitivity for couples of Hamiltonians, Journal of Dynamical and Control Systems, 19, 4, p. 593-610. http://dx.doi.org/10.1007/s10883-013-9197-0

Type
Article accepté pour publication ou publié
External document link
http://fr.arxiv.org/abs/1301.1020
Date
2013
Journal name
Journal of Dynamical and Control Systems
Volume
19
Number
4
Publisher
Springer
Pages
593-610
Publication identifier
Metadata
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Author(s)
Mandorino, Vito
Abstract (EN)
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.
Subjects / Keywords
Rectifiable set of positive codimension; Thom transversality theorem; Reachable set; Controllability; Hamiltonian system; Switched system