TY - JOUR
TI - An effective approach to Picard-Vessiot theory and the Jacobian Conjecture
AU - Bogdan, Paweł
AU - Hajto, Zbigniew
AU - Adamus, Elżbieta
TI - An effective approach to Picard-Vessiot theory and the Jacobian Conjecture
AB - 
	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
VL - 2017
IS - Volume 26
PY - 2018
SN - 1732-3916
C1 - 2083-8476
SP - 49
EP - 60
DO - 10.4467/20838476SI.17.004.8150
UR - https://ejournals.eu/en/journal/schedae-informaticae/article/an-effective-approach-to-picard-vessiot-theory-and-the-jacobian-conjecture
KW - Picard-Vessiot theory
KW - Polynomial mapping
KW - Jacobian Conjecture