Resumen de Analytic varieties as limit periodic sets

André Belotto da Silva

• Let f(x,y)≢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}∩BR((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.