LLORENS, M. Nicolas (2024) Ensembles avec une normale constante dans les groupes de Carnot : une approche par contrôle géométrique PRE - Research Project, ENSTA.
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Abstract
This text explores certain geometric properties of Carnot groups, based on an article published in 2020 by C. Bellettini and E. Le Donne titled : Sets with constant normal in Carnot groups : properties and examples. We begin by reintroducing the notions of Carnot groups, half-spaces, and the associated semigroup, which we relate to the reachable sets of affine controlled systems. We then present general results from control theory before studying the controllability of our system, particularly through the example of Heisenberg groups. Furthermore, we examine in more detail the properties of the drift-free system’s orbit when it is of codimension 1, leading us to a more precise description of a result from the article by C. Bellettini and E. Le Donne.
Item Type: | Thesis (PRE - Research Project) |
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Uncontrolled Keywords: | Carnot group, controlled system, reachable set, orbit, Lie algebra, controllability, Heisenberg group, immersed/embedded submanifold, exponential coordinates. |
Subjects: | Mathematics and Applications |
ID Code: | 10203 |
Deposited By: | Nicolas LLORENS |
Deposited On: | 02 sept. 2024 17:39 |
Dernière modification: | 02 sept. 2024 17:39 |
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