Slow Divergence Integrals in Classical Liénard Equations Near Centers

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• 作者：Peter De Maesschalck ; Renato Huzak
• 关键词：Classical Liénard equations ; Limit cycles ; Singular perturbations ; Slow ; fast systems ; Slow divergence integral
• 刊名：Journal of Dynamics and Differential Equations
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：27
• 期：1
• 页码：177-185
• 全文大小：208 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Ordinary Differential Equations
  Partial Differential Equations
  Applications of Mathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9222

文摘

We significantly improve lower bounds for the number of limit cycles for polynomial classical Liénard equations, aiming at stating lower bounds that are reasonable enough to be optimal. The techniques used are the notion of slow divergence integral from the geometric theory of planar slow-fast systems.