周期环的周期性与Bautin理想的原则化
Cyclicity of period annuli and principalization of Bautin ideals
摘要：
证明了在给定解析向量场的多参数解析变形下，从一个开周期环分支出的极限环的最大数目与在适当的单参数解析变形下的相同，只要这个环的周期性是有限的.沿着同样的路线，我们也给出了同宿鞍环的圈性的一个界。
英文摘要：
We prove that the maximal number of limit cycles which bifurcate from an open period annulus under a given multi-parameter analytic deformation of a given analytic vector field is the same as in an appropriate one-parameter analytic deformation of the field, provided that this cyclicity is finite. Along the same lines we give also a bound of the cyclicity of homoclinic saddle loops.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
