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A theorem on generic intersections in an o-minimal structure

Krzysztof Jan Nowak (2014)

Fundamenta Mathematicae

Consider a transitive definable action of a Lie group G on a definable manifold M. Given two (locally) definable subsets A and B of M, we prove that the dimension of the intersection σ(A) ∩ B is not greater than the expected one for a generic σ ∈ G.

An estimation of the controllability time for single-input systems on compact Lie Groups

Andrei Agrachev, Thomas Chambrion (2006)

ESAIM: Control, Optimisation and Calculus of Variations

Geometric control theory and Riemannian techniques are used to describe the reachable set at time t 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...

An introduction to loopoids

Janusz Grabowski (2016)

Commentationes Mathematicae Universitatis Carolinae

We discuss a concept of loopoid as a non-associative generalization of Brandt groupoid. We introduce and study also an interesting class of more general objects which we call semiloopoids. A differential version of loopoids is intended as a framework for Lagrangian discrete mechanics.

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