Geometric control theory and Riemannian techniques are used to describe
the reachable set at time of left invariant single-input control systems
on semi-simple compact Lie groups and to
estimate the minimal time needed to reach any point from identity.
This method provides an effective way to give an upper and a lower bound
for the minimal time needed to transfer a controlled quantum system
with a drift from a given initial position to a given final position.
The bounds include diameters...
We study Hamiltonian systems which generate extremal flows of regular
variational problems on smooth manifolds and demonstrate that
negativity of the generalized curvature of such a system implies
the existence of a global smooth optimal synthesis for the infinite
horizon problem.
We also show that in the Euclidean case negativity of the generalized curvature is a consequence of
the convexity of the Lagrangian with respect to the pair of arguments. Finally, we give a generic classification for...
We study sub-Riemannian (Carnot-Caratheodory) metrics defined by
noninvolutive distributions on real-analytic Riemannian manifolds.
We establish a connection between regularity properties of these
metrics and the lack of length minimizing abnormal geodesics.
Utilizing the results of the previous study of abnormal length
minimizers accomplished by the authors in [Annales IHP. , p. 635-690] we describe in this
paper two classes of the germs of distributions (called
2-generating and medium fat) such...
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