Transient fractal behavior in snapshot attractors of driven chaotic systems

Snapshot attractors, i.e., attractors formed by a cloud of trajectories at the same instants of time, are usually employed to reveal the fractal structure of randomly or chaotically driven dynamical systems. A necessary condition for the underlying fractal structure to be observed is that the ensemble of particles utilized in the construction of the snapshot attractors are subject to identical perturbation at any instant of time. We examine the influence of small phase-space inhomogeneity in the chaotic perturbation on the observability of the snapshot fractal attractors. We find that, typically, fractal structure can be seen in only a transient period of time. The scaling of the transient time with the amount of inhomogeneity is investigated. Implication to experimental observation of fractal structure in physical systems is pointed out.