Orbit equivalence of linear systems on manifolds and semigroup actions on homogeneous spaces

TL;DR

This paper introduces orbit equivalence for semigroup actions and generalized linear control systems on manifolds, showing under certain conditions their systems are equivalent to linear control systems on homogeneous spaces.

Contribution

It establishes a connection between generalized linear control systems on manifolds and linear control systems on homogeneous spaces through orbit equivalence.

Findings

Semigroup systems of generalized linear control systems are orbit equivalent to those on homogeneous spaces.

Provides conditions under which orbit equivalence holds.

Extends the theory of control systems on manifolds and homogeneous spaces.

Abstract

In this paper we introduce the notion of orbit equivalence for semigroup actions and the concept of generalized linear control system on smooth manifold. The main goal is to prove that, under certain conditions, the semigroup system of a generalized linear control system on a smooth manifold is orbit equivalent to the semigroup system of a linear control system on a homogeneous space.