%0 Journal Article
%T An effective approach to Picard-Vessiot theory and the Jacobian Conjecture
%A Bogdan, Paweł
%A Hajto, Zbigniew
%A Adamus, Elżbieta
%J Schedae Informaticae
%V 2017
%R 10.4467/20838476SI.17.004.8150
%N Volume 26
%P 49-60
%K Picard-Vessiot theory, Polynomial mapping, Jacobian Conjecture
%@ 1732-3916
%D 2018
%U https://ejournals.eu/en/journal/schedae-informaticae/article/an-effective-approach-to-picard-vessiot-theory-and-the-jacobian-conjecture
%X 
	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. Drużkowski