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RESEARCH PRODUCT
Generic properties of singular trajectories
Bernard BonnardI. A. K. Kupkasubject
Pure mathematicsDense setGeneric propertyApplied MathematicsRank (differential topology)TopologyManifoldSingularityBounded functionOrder (group theory)Vector fieldMathematical PhysicsAnalysisMathematicsdescription
Abstract Let M be a σ-compact C∞ manifold of dimension d ≥ 3. Consider on M a single-input control system : x (t) = F 0 (x(t)) + u(t) F 1 (x(t)) , where F0, F1 are C∞ vector fields on M and the set of admissible controls U is the set of bounded measurable mappings u : [0Tu]↦ R , Tu > 0. A singular trajectory is an output corresponding to a control such that the differential of the input-output mapping is not of maximal rank. In this article we show that for an open dense subset of the set of pairs of vector fields (F0, F1), endowed with the C∞-Whitney topology, all the singular trajectories are with minimal order and the corank of the singularity is one.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1997-01-01 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis |