In dissipative systems without any driving or positive feedback all motion stops ultimately since the initial kinetic energy is dissipated away during time evolution. If chaos is present, it can only be of transient type. Traditional transient chaos is, however, supported by an infinity of unstable orbits. In the lack of these, chaos in undriven dissipative systems is of another type: it is termed doubly transient chaos as the strength of transient chaos is diminishing in time, and ceases asymptotically. Here we show that a clear view of such dynamics is provided by identifying KAM tori or chaotic regions of the dissipation-free case, and following their time evolution in the dissipative dynamics. The tori often smoothly deform first, but later they become disintegrated and dissolve in a kind of shrinking chaos. We identify different dynamical measures for the characterization of this process which illustrate that the strength of chaos is first diminishing, and after a while disappears, the motion enters the phase of ultimate stopping.

在没有任何驱动或正反馈的耗散系统中，所有运动最终都会停止，因为初始动能在时间演化过程中被耗散。如果存在混沌，它只能是瞬态类型。然而，传统的瞬态混沌得到了无限不稳定轨道的支持。在缺乏这些的情况下，无驱动耗散系统中的混沌是另一种类型：它被称为双瞬态混沌，因为瞬态混沌的强度随时间递减，并逐渐停止。在这里，我们表明通过识别无耗散情况的 KAM 环面或混沌区域，并跟踪它们在耗散动力学中的时间演变，可以清楚地了解这种动力学。环面通常先是平滑地变形，但后来它们会解体并溶解在一种收缩的混乱中。