Analytic varieties as limit periodic sets

• Autores: André Belotto da Silva
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 11, Nº 2, 2012, págs. 449-465
• Idioma: inglés
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• Resumen

  • 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.

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