Qualitative Theory of Dynamical Systems

, Volume 11, Issue 2, pp 449–465 | Cite as

Analytic Varieties as Limit Periodic Sets

  • André Belotto


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.


Periodic Orbit Implicit Function Theorem Analytic Family Connected Part Planar Vector 
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© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et Applications, Faculté des Sciences et TechniquesUniversité de Haute-AlsaceMulhouseFrance

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