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Dynamics of LCSs on the group of proper motions
Victor Ayala, Adriano Da Silva, Alejandro Otero Robles
This article describes the control behavior of any linear control systems on the group of proper motions . It characterizes the controllability property and the control sets…
Control sets of linear systems on semi-simple Lie groups
Victor Ayala, Adriano Da Silva, Philippe Jouan +1
In this paper we study the main properties of control sets with nonempty interior of linear control systems on semisimple Lie groups. We show that, unlike the solvable case, linear…
The control set of a linear control system on the two dimensional solvable Lie group
Victor Ayala, Adriano Da Silva
In this paper we explicitly calculate the control sets associated with a linear control system on the two dimensional solvable Lie group. We show that a linear control system of su…
On the characterization of the controllability property for linear control systems on nonnilpotent, solvable three-dimensional Lie groups
Victor Ayala, Adriano Da Silva
In this paper we show that a complete characterization of the controllability property for linear control system on three-dimensional solvable nonnilpotent Lie groups is possible b…
Isometries of almost-Riemannian structures on Lie groups
Philippe Jouan, Zsigmond Guilherme, Victor Ayala
A simple Almost-Riemannian Structure on a Lie group G is defined by a linear vector field (that is an infinitesimal automorphism) and dim(G) -- 1 left-invariant ones. It is first p…