2015/06/04 by Elżbieta Adamus, Adamus, Elzbieta, Pawel Bogdan +5
Engineering · Mathematics · Physics and Astronomy · #14R10 #14R15 #Advanced Differential Equations and Dynamical Systems #Commutative Algebra (math.AC) #Control and Dynamics of Mobile Robots #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math.AC #msc:14R10 #msc:14R15
paper · pdf · doi:10.48550/arxiv.1506.01662
arxiv created 2015/06/04 · openalex publication_date 2015/06/04 · arxiv updated 2015/06/05 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
In this paper we present a theorem concerning an equivalent statement of the Jacobian Conjecture in terms of Picard-Vessiot extensions. Our theorem completes the earlier work of T. Crespo and Z. Hajto which suggested an effective criterion for detecting polynomial automorphisms of affine spaces. We show a simplified criterion and give a bound on the number of wronskians determinants which we need to consider in order to check if a given polynomial mapping with non-zero constant Jacobian determinant is a polynomial automorphism. Our method is specially efficient with cubic homogeneous mappings introduced and studied in fundamental papers by H. Bass, E. Connell, D. Wright and L. Druzkowski.