Preprint Article Version 1 This version is not peer-reviewed

Contribution to the Jacobian Conjecture: Polynomial Mapping Having Two Zeros at Infinity

Version 1 : Received: 17 July 2018 / Approved: 17 July 2018 / Online: 17 July 2018 (12:04:11 CEST)

How to cite: Biernat, G.; Lara-Dziembek, S..; Pawlak, E.. Contribution to the Jacobian Conjecture: Polynomial Mapping Having Two Zeros at Infinity. Preprints 2018, 2018070311 (doi: 10.20944/preprints201807.0311.v1). Biernat, G.; Lara-Dziembek, S..; Pawlak, E.. Contribution to the Jacobian Conjecture: Polynomial Mapping Having Two Zeros at Infinity. Preprints 2018, 2018070311 (doi: 10.20944/preprints201807.0311.v1).

Abstract

This article contains the theorems concerning the algebraic dependence of polynomial mappings with the constant Jacobian having two zeros at infinity. The work is related to the issues of the classical Jacobian Conjecture. This hypothesis affirm that the polynomial mapping of two complex variables with constant non-zero Jacobian is invertible. The Jacobian Conjecture is equivalent to the fact that polynomial mappings with constant non-zero Jacobian do not have two zeros at infinity, therefore it is equivalent to the two theorems given in the work. The proofs of these theorems proceeds by induction.

Subject Areas

Zeros at infinity, Jacobian Conjecture

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