Abstract
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 \({\{f(x, y)=0\} \cap \overline{B_R((0, 0))}}\) as a limit periodic set. Furthermore, we show that if f(x, y) is polynomial, then there exists a polynomial family with these properties.
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Belotto, A. Analytic Varieties as Limit Periodic Sets. Qual. Theory Dyn. Syst. 11, 449–465 (2012). https://doi.org/10.1007/s12346-012-0070-4
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DOI: https://doi.org/10.1007/s12346-012-0070-4