In this note we introduce the V-shaped action functional with delay in a symplectization, which is an intermediate action functional between the Rabinowitz action functional and the V-shaped action functional. It lives on the same space as the V-shaped action functional, but its gradient flow equation is a delay equation as in the case of the Rabinowitz action functional. We show that there is a smooth interpolation between the V-shaped action functional and the V-shaped action functional with delay during which the critical points and its actions are fixed. Moreover, we prove that there is a bijection between gradient flow lines of the V-shaped action functional with delay and the ones of the Rabinowitz action functional.

在本文中，我们介绍了在辛化中具有延迟的 V 形动作泛函，它是 Rabinowitz 动作泛函和 V 形动作泛函之间的中间动作泛函。它与 V 形作用泛函位于同一空间，但其梯度流方程是延迟方程，与拉比诺维茨作用泛函的情况一样。我们表明，在 V 形动作泛函和具有延迟的 V 形动作泛函之间存在平滑插值，在此期间，关键点及其动作是固定的。此外，我们证明了具有延迟的 V 形动作泛函的梯度流线与 Rabinowitz 动作泛函的梯度流线之间存在双射。