In this article, we propose a control law for almostglobal asymptotic tracking (AGAT) of a smooth reference trajectory for a fully actuated simple mechanical system (SMS) evolving on a Riemannian manifold which can be embedded in a Euclidean space. The existing results on tracking for an SMS are either local, or almost-global, only in the case the manifold is a Lie group. In the latter case, th...

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot–Caratheodory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on...

Regular almost periodicity in compact minimal abelian flows was characterized for the case of discrete acting group by W. Gottschalk and G. Hedlund and for the case of 0-dimensional phase space by W. Gottschalk a few decades ago. In 1995 J. Egawa gave characterizations for the case when the acting group is R. We extend Egawa’s results to the case of an arbitrary abelian acting group and a not n...

We prove that for any collection F of n ≥ 2 pairwise disjoint compact convex sets in the plane there is a pair A and B such line separates from either or subcollection with at least /18 sets.

This paper holds to establish a soft pre-compact map and investigate its associations with maps, almost A-almost compact A*-almost mildly semi-compact M-mildly maps besides M*-mildly which are utilized from the relations between their spaces under some conditions or without conditions. Consequently, composition factors of studied based on previous association them. Many examples given explain r...