Purely decaying systems: the transient charm of decaying chaos

Purely decaying systems: the transient charm of decaying chaos

The long-term behavior of damped, unforced systems is very simple: due to energy dissipation, all motion eventually ceases. Consequently, if the motion is chaotic, it can only remain chaotic for a finite time. This behavior has previously been identified with the phenomenon of conventional transient chaos; however, a defining feature of typical transient chaos is that an infinite number of perpetually moving trajectories form a fractal set, among which typical trajectories wander. In damped, unforced systems no perpetually moving trajectories exist, and therefore a different type of description is required. Our goal is to provide a detailed theoretical characterization of this behavior, based on tracking the continuously decreasing energy of the system.

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