平面上一类新的非内射多项式局部自同态
A new class of non-injective polynomial local diffeomorphisms on the plane
摘要：
在这个简短的说明中，我们提供了迄今为止已知的非内射局部多项式同构$F=(p,q):\mathbb{R}^2 \to \mathbb{R}^2$的最低阶的例子。在我们的示例中，$p$具有度$10$，并且$q$具有度$15$，而不是分别为$10$和$25$的度，到目前为止，这两个度被认为是$F$的坐标的最小度。我们的结构是基于S。平丘克庆祝反例真正的雅可比猜想。
英文摘要：
In this short note we provide the example with the lowest degree known so far of a non-injective local polynomial diffeomorphism $F=(p,q):\mathbb{R}^2 \to \mathbb{R}^2$. In our example $p$ has degree $10$ and $q$ has degree $15$, rather than $10$ and $25$, respectively, known up to now as the smallest degrees for the coordinates of $F$. Our construction was based on S. Pinchuk celebrated counterexample to the real Jacobian conjecture.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
