6 papers
The General Solution for Affine Control Systems on Lie Groups
João Paulo Lima de Oliveira, Alexandre José Santana, Simão Nicolau Stelmastchuk
The purpose of this paper is to present explicitly the solution curve for affine control systems on Lie groups under the assumption that automorphisms associated to the linear vect…
Periodic orbits of Linear and invariant flows on connected Lie groups
S. N. Stelmastchuk
Our main is to study periodic orbits of linear and invariant flows on a real, connected Lie group. Since each linear flow has a derivation associated , we show t…
Solution Curve for Linear Control Systems on Lie Groups
João Paulo Lima de Oliveira, Alexandre J. Santana, Simão N. Stelmastchuk
The purpose of this paper is to describe explicitly the solution for linear control systems on Lie groups. In case of linear control systems with inner derivations, the solution is…
Linear flows on compact, semisimple Lie groups: stability, periodic orbits, and Poincaré-Bendixon's Theorem
S. N. Stelmastchuk
Our first purpose is to study the stability of linear flows on real, connected, compact, semisimple Lie groups. After, we study and classify periodic orbits of linear and invariant…
A topological conjugacy of invariant flows on some class of Lie groups
Alexandre J. Santana, Simão N. Stelmastchuk
The aim of this paper is to give a condition to topological conjugacy of invariant flows in an Lie group which its Lie algebra is associative algebra or semisimp…
Transport Theorem and Continuity Equations: a Stochastic Approach
Pedro Catuogno, Simão N. Stelmastchuk
We give a stochastic generalization of transport theorem on smooth manifold. Furthermore, we deduce a system of continuity equation and present some application on torus.