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Local controllability for families of diffeomorphisms. (English) Zbl 0778.93003

Summary: We study groups and semigroups which are generated by analytic families of diffeomorphisms. The central notion is that of local controllability of a family of diffeomorphisms at a given point of the state manifold, when generalizes the familiar notion of local controllability of control systems with continuous, as well as discrete time. Lie theory methods are used. We systematically exploit the so-called fast switching variations and properties of the jet spaces of curves on the state manifold.

MSC:

93B05 Controllability
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