Pinchuk平面多项式对的作图
Picturing Pinchuk's Plane Polynomial Pair
摘要：
谢尔盖·平丘克发现了一类两个变量的实多项式对，它们有一个无处消失的雅可比行列式，并定义了实平面到其自身的非一一对应的映射。本文描述了一类特殊映射的渐近性态。所呈现的详细程度使地图具有良好的几何视觉效果。纠正了先前对地图图像描述中的错误（图像的补充由两个点组成，而不是四个点）。由于Ronen Peretz的技术被用来验证描述的渐近变化的地图。
英文摘要：
Sergey Pinchuk discovered a class of pairs of real polynomials in two variables that have a nowhere vanishing Jacobian determinant and define maps of the real plane to itself that are not one-to-one. This paper describes the asymptotic behavior of one specific map in that class. The level of detail presented permits a good geometric visualization of the map. Errors in an earlier description of the image of the map are corrected (the complement of the image consists of two, not four, points). Techniques due to Ronen Peretz are used to verify the description of the asymptotic variety of the map.
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。
