On a tropical version of the Jacobian conjecture. (March 2022)

• Record Type: Journal Article
• Authors: Grigoriev, Dima; Radchenko, Danylo
• Is Part Of: Journal of symbolic computation. Volume 109(2022)
• Page Start: 399
• Page End: 403
• Publication Date: 2022-03
• Subjects: 14T05; Tropical Jacobian conjecture -- Tropical rational mappings; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.07.012
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We prove that, for a tropical rational map if for any point the convex hull of Jacobian matrices at smooth points in a neighborhood of the point does not contain singular matrices then the map is an isomorphism. We also show that a tropical polynomial map on the plane is an isomorphism if all the Jacobians have the same sign (positive or negative). In addition, for a tropical rational map we prove that if the Jacobians have the same sign and if its preimage is a singleton at least at one regular point then the map is an isomorphism.