2019/01/27 by Müllhaupt, Philippe
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #93B52 53D17 58H05 13P15 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Nonlinear Waves and Solitons #Optimization and Control (math.OC) #Sphingolipid Metabolism and Signaling #math.OC #msc:13P15 #msc:53D17 #msc:58H05 #msc:93B52
paper · pdf · doi:10.48550/arxiv.1901.09420
Extended version of a 6 pages paper for the NOLCOS 2019 conference paper
arxiv created 2019/01/27 · openalex publication_date 2019/01/27 · arxiv updated 2019/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two Lie algebroids are presented that are linked to the construction of the linearizing output of an affine in the input nonlinear system. The algorithmic construction of the linearizing output proceeds inductively, and each stage has two structures, namely a codimension one foliation defined through an integrable 1-form ω , and a transversal vectorfield g to the foliation. Each integral manifold of the vectorfield g defines an equivalence class of points. Due to transversality, a leaf of the foliation is chosen to represent these equivalence classes. A Lie groupoid is defined with its base given as the particular chosen leaf and with the product induced by the pseudogroup of diffeomorphisms that preserve equivalence classes generated by the integral manifolds of g. Two Lie algebroids associated with this groupoid are then defined. The theory is illustrated with an example using polynomial automorphisms as particular cases of diffeomorphisms and shows the relation with the Jacobian conjecture.