Analytic varieties as limit periodic sets

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 $X_{\lambda}$ which has $\{f(x,y)=0\} \cap \bar{B_R((0,0))}$ as limit periodic set. Furthermore, we that if $f(x,y)$ is polynomial, then polynomial with these properties.