一般Hopf-零奇点的指数小异宿崩溃
Exponentially small heteroclinic breakdown in the generic Hopf-zero singularity
摘要：
本文证明了在参数空间的开集上一般的Hopf-零奇点的解析开折中异宿联络的破裂。这种异宿轨道出现在任何顺序，如果一个执行正常形式周围的原点，因此它是一个现象“超越所有订单”。本文给出了一维稳定流形和一维不稳定流形之间的距离公式，该距离由扰动参数中的指数小函数给出。我们的结果适用于保守和耗散的开折。
英文摘要：
In this paper we prove the breakdown of an heteroclinic connection in the analytic versal unfoldings of the generic Hopf-Zero singularity in an open set of the parameter space. This heteroclinic orbit appears at any order if one performs the normal form around the origin, therefore it is a phenomenon "beyond all orders". In this paper we provide a formula for the distance between the corresponding stable and unstable one dimensional manifolds which is given by an exponentially small function in the perturbation parameter. Our result applies both for conservative and dissipative unfoldings.
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