The ionization of hydrogen in a circularly polarized electric field consists of the electron escaping over a rotating Stark saddle. The escape is mediated by the stable and unstable manifolds of a normally hyperbolic invariant manifold associated with the saddle. General principles guarantee the existence of this normally hyperbolic invariant manifold which is referred to as a transition state for energies close to the saddle. We use a numerical procedure to continue the transition state to high energies and study the dynamics restricted to the transition state. We find that for the strength of the electric field under consideration, the transition state persists to very high energies and the restricted dynamics remains amazingly regular. Our analysis moreover includes a study of homoclinic orbits connecting the transition state to itself.

中文翻译：

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与控制圆极化电场中氢电离的正常双曲线不变流形相关的动力学

圆极化电场中氢的电离包括电子在旋转的​​斯塔克鞍上逃逸。逃逸是由与鞍座相关的正常双曲不变流形的稳定和不稳定流形介导的。一般原理保证了这种通常双曲不变的流形的存在，它被称为接近鞍的能量的过渡态。我们使用数值程序将过渡态继续到高能，并研究限制在过渡态的动力学。我们发现，对于所考虑的电场强度，过渡态持续到非常高的能量，并且受限的动力学仍然非常规律。我们的分析还包括对连接过渡态与其自身的同宿轨道的研究。