Verification of the Jacobian Conjecture for d-linear maps in two\n variables

2021/11/20 by Mario DeFranco, DeFranco, Mario
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Control and Dynamics of Mobile Robots #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2111.10739

openalex publication_date 2021/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any integer d \≥ 1, we verify the Jacobian Conjecture for a\nd-linear map in two variables. We prove that almost all the coefficients of\nthe formal inverse are in the ideal specified by the Jacobian condition. We\nfind expressions for certain elements in terms of the generators of this ideal.\nTo obtain these expressions, we generalize a bijective proof of the\nCayley-Hamilton theorem in two ways.\n

Related

• On the Jacobian Conjecture and ideal membership for degree d-linear maps
• The Jacobian conjecture
• An Optimization Approach to Jacobian Conjecture
• Generalizations of local bijectivity of Keller maps and a proof of 2-dimensional Jacobian conjecture
• Some Remarks on the Jacobian Conjecture and Connections with Hilbert's Irreducibility Theorem