Abstract
In this chapter we study general properties of attainable sets. We consider families of vector fields F on a smooth manifold M that satisfy the property $$Li{e_q}F = {T_q}M\forall q \in M.$$ (8.1) In this case the system F is called bracket-generating, or full-rank. By the analytic version of the Orbit Theorem (Corollary 5.17), orbits of a bracket-generating system are open subsets of the state space M.KeywordsVector FieldPhase PortraitSmooth ManifoldInitial SystemCompatible VectorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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