作为极限周期集的解析簇
Analytic varieties as limit periodic sets
摘要：
设$f(x,y) \not\equiv 0$为实解析平面函数。我们证明了，对于几乎每一个$R>0$存在一个解析的1-参数族的向量场$X_λ$有$\{f(x,y)=0\} \cap \bar{B_R((0,0))}$作为一个极限周期集。进一步证明了如果$f(x,y)$是多项式，则存在具有这些性质的多项式族.
英文摘要：
Let $f(x,y) \not\equiv 0$ be a real-analytic planar function. We show that, for almost every $R>0$ there exists an analytic 1-parameter family of vector fields $X_λ$ which has $\{f(x,y)=0\} \cap \bar{B_R((0,0))}$ as a limit periodic set. Furthermore, we show that if $f(x,y)$ is polynomial, then there exists a polynomial family with these properties.
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。
