二维异宿联络在Hopf零奇点下的破缺（I）
Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity (I)
摘要：
本文研究了Hopf零奇性解析开折中出现的一种超越所有阶的现象。它包括在一个二维异宿曲面的故障存在于截断的正常形式的这个奇异性在任何顺序。在本文中的结果是双重的：一方面，我们给出的结果一般的开折，导致尖锐的指数小上界的差异，这些流形。另一方面，我们提供的Melnikov函数的一些非通用的开折的这种差异的渐近公式。
英文摘要：
In this paper we study a beyond all order phenomenon which appears in the analytic unfoldings of the Hopf-zero singularity. It consists in the breakdown of a two-dimensional heteroclinic surface which exists in the truncated normal form of this singularity at any order. The results in this paper are twofold: on the one hand we give results for generic unfoldings which lead to sharp exponentially small upper bounds of the difference between these manifolds. On the other hand, we provide asymptotic formulas for this difference by means of the Melnikov function for some non-generic unfoldings.
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。
