Arnold的$J^+$ -不变量
Introduction to Arnold's $J^+$-Invariant
摘要：
我们探讨阿诺德的$J^+$不变的浸入-平面光滑闭曲线的非零导数，在最多的二重点，只有横截相交-和计算方法，如维罗的总和，等等。只有基本的本科数学是需要理解这篇介绍性论文的内容和一切，我们需要的是上面的回忆或介绍。包括示例、练习和解决方案以供练习。
英文摘要：
We explore Arnold's $J^+$-invariant of immersions -- planar smooth closed curves with non-vanishing derivative, at most double points and only transverse intersections -- and computation methods like Viro's sum, among others. Only basic undergraduate mathematics is needed to understand the contents of this introductory paper and everything we need that is above that is recalled or introduced. Examples, exercises and solutions are included for practice.
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。
