论文标题
雅各布猜想的优化方法
An Optimization Approach to Jacobian Conjecture
论文作者
论文摘要
令$ n \ geq 2 $和$ \ mathbb k $为特征$ 0 $的数字字段。 Jacobian猜想对多项式地图$ \ MATHCAL P $从$ \ Mathbb k ^n $开始，如果其雅各布矩阵的决定因素是$ \ mathbb k $中的非零常数，则iNverse $ \ \ \ \ m m iatscal p ^{ - 1} $也是一张polynom alsial Map。凯勒（Keller）于1939年首先提出了这一猜想，以$ \ mathbb k ^n = \ mathbb c ^2 $提出，并列入了Smale 1998年的下一世纪数学问题清单。这项研究将为猜想提供证据。我们的证明基于dru {} kowski地图和哈达玛德的差异定理，并还使用了一些优化的想法。
Let $n\geq 2$ and $\mathbb K $ be a number field of characteristic $0$. Jacobian Conjecture asserts for a polynomial map $\mathcal P$ from $\mathbb K ^n$ to itself, if the determinant of its Jacobian matrix is a nonzero constant in $\mathbb K $ then the inverse $\mathcal P^{-1}$ exists and is also a polynomial map. This conjecture was firstly proposed by Keller in 1939 for $\mathbb K ^n=\mathbb C^2$ and put in Smale's 1998 list of Mathematical Problems for the Next Century. This study is going to present a proof for the conjecture. Our proof is based on Dru{ż}kowski Map and Hadamard's Diffeomorphism Theorem, and additionally uses some optimization idea.
