Reduction theorems for the strong real Jacobian conjecture (Q2872669)

The author presents reductions of polynomial mappings \(F:\mathbb{K} ^{n}\rightarrow \mathbb{K}^{n}\) (\(\mathbb{K=R}\) or \(\mathbb{C}\)) to the simpler ones using various notions of equivalences. The reductions are implementations of the known classic reductions (proved under some assumptions on the Jacobian of \(F\)) connected to the Jacobian Conjecture:NEWLINENEWLINE to the Yagzhev map \(F=X+H\) -- each component of \(H\) is a cubic homogeneous polynomial,NEWLINENEWLINE to the Drużkowski map \(F=X+H\) -- each component of \(H\) is the cube of a linear form and to the symmetric map which means the Jacobi matrix \(J(F)\) is symmetric.