Attainable Sets

  • Andrei A. Agrachev
  • Yuri L. Sachkov
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 87)


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
$$Li{e_q}F = {T_q}M\forall q \in M.$$
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.


Vector Field Phase Portrait Smooth Manifold Initial System Compatible Vector 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Andrei A. Agrachev
    • 1
  • Yuri L. Sachkov
    • 2
  1. 1.SISSA-ISASTriesteItaly
  2. 2.Program Systems InstitutePereslavl-ZalesskyRussia

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