Citation
B. Bonnard et I. Kupka, 2 GENERIC PROPERTIES FOR SINGULAR TRAJECT ORIES, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 319(5), 1994, pp. 509-512
Citations number
8
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
ISSN journal
07644442
Volume
319
Issue
5
Year of publication
1994
Pages
509 - 512
Database
ISI
SICI code
0764-4442(1994)319:5<509:2GPFST>2.0.ZU;2-X
Abstract
Let M be a C-infinity, second countable manifold and consider on M a s
ingle-input control system: x(t) = F-0(x(t)) + u(t)F-1(x(t)), where F-
0, F-1 are C-infinity vector fields and the set of admissible controls
U is the set of bounded, measurable mappings u : [0, T (u)] --> R, T
(u) > 0. In this article we show that for an open dense subset of the
the set of pairs of vector fields (F-0, F-1), endowed with the C-infin
ity-Whitney topology, all the singular trajectories are of minimal ord
er and normal.