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Qualitative Theory of Dynamical Systems

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

Analytic Varieties as Limit Periodic Sets

  • André Belotto
Article

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.

Keywords

Periodic Orbit Implicit Function Theorem Analytic Family Connected Part Planar Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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