S. Stelmastchuk

activity

20092026

collaborators

20 papers

math.DS2026

Algebraic Conjugacy of Linear Flows on Connected Lie Groups

S. N. Stelmastchuk

We study algebraic conjugacy of linear flows on connected Lie groups. To each linear flow we associate a derivation of the Lie algebra, and we analyze how the conjugacy problem can…

math.OC2026

Vertical Control Systems on Tangent Bundles and Fiberwise Controllability

S. N. Stelmastchuk

We study control systems on the tangent bundle of a smooth manifold induced by vertical lifts of vector fields. The Vertical dynamics acts exclusively along the fibers, leaving the…

math.OC2025

Projective Controllability of Complete Lifted Control Systems

S. N. Stelmastchuk

We introduce the complete lifted control system associated with a control system on a smooth manifold by replacing each vector field with its complete lift to the tangent bundle. W…

math.PR2022

Martingales on Principal Fiber Bundles

Pedro Catuogno, Simão N. Stelmastchuk

Let $P (M, G)$ be a principal fiber bundle, let $ω$ be a connection form on $P (M, G)$ , and consider a projectable connection $\nabla^{P}$ on $P (M, G)$ . The aim of this work is to deter…

math.OC2020

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…

math.DS2020

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 $φ_{t}$ has a derivation associated $D$ , we show t…

math.OC2019

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…

math.DS2018

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…

math.OC2017

Controllability of Linear Control Systems on Solvable Lie Groups with Hyperbolic Drift

S. N. Stelmastchuk

We study the controllability of linear control systems on connected solvable Lie groups with hyperbolic drift. Under a suitable splitting assumption on the control directions, we s…

math.DS2016

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 $G$ which its Lie algebra $g$ is associative algebra or semisimp…

math.DG2015

A factorization of harmonic maps into Semisimple Lie groups

Simão N. Stelmastchuk

We factorize harmonic maps with values in a semisimple Lie groups in a product of harmonic maps with values in the components of the Iwasawa decomposition. In particular, we use th…

math.PR2015

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.

math.DG2014

Harmonic Maps into Homogeneous Spaces According to a Darboux Homogeneous Derivative

Alexandre J. Santana, Simão N. Stelmastchuk

Our purpose is to use a Darboux homogenous derivative to understand the harmonic maps with values in homogeneous space. We present a characterization of these harmonic maps from th…

math.PR2011

Vertical martingales, stochastic calculus and harmonic sections

Simão Stelmastchuk

This work is about a new class of martingales: the vertical martingales. We construct the vertical martingale for smooth submersions and we develop a stochastic calculus for one. F…

math.PR2011

Martingales in Reductive Homogeneous spaces

S. N. Stelmastchuk

The subject of this work is to study martingales in a reductive homogeneous space with respect to a symmetric connection. Our basic idea is to view homogenous spaces as principal f…

math.PR2011

The Itô exponential on Lie Groups

Simão N. Stelmastchuk

Let $G$ be a Lie Group with a left invariant connection $\nabla^{G}$ . Denote by $\g$ the Lie algebra of $G$ , which is equipped with a connection $\nabla^{\g}$. Our main is to intro…

math.DG2009

A Pluzhnikov's Theorem, Brownian motions and Martingales in Lie Group with skew-symmetric connections

S. N. Stelmastchuk

Let $G$ be a Lie Group with a left invariant connection such that its connection function is skew-symmetric. Our main goal is to show a version of Pluzhnikov's Theorem for this kin…

math.DG2009

An equivalence between harmonic sections and sections that are harmonic maps

S. N. Stelmastchuk

Let $π : (E, \nabla^{E}) \to (M, g)$ be an affine submersion with horizontal distribution, where $\nabla^{E}$ is a symmetric connection and $M$ is a Riemannian manifold. Let $σ$ be a s…

math.DG2009

A characterization of Einstein manifolds

S. N. Stelmastchuk

In this work we wish characterize the Einstein manifolds $(M, g)$ , however without the necessity of hypothesis of compactness over $M$ and unitary volume of $g$ , which are well know…

math.DG2009

Stochastic characterization of harmonic sections and a Liouville theorem

S. N. Stelmastchuk

Let $P (M, G)$ be a principal fiber bundle and $E (M, N, G, P)$ be an associate fiber bundle. Our interested is to study harmonic sections of the projection $π_{E}$ of $E$ into $M$ . Our…