title: Universal and nonuniversal features in shadowing dynamics of nonhyperbolic chaotic systems with unstable-dimension variability.
abstract: An important quantity characterizing the shadowability of computer-generated trajectories in nonhyperbolic chaotic system is the shadowing time, which measures for how long a numerical trajectory remains valid. This time depends sensitively on an initial condition. Here, we show that for nonhyperbolic systems with unstable-dimension variability, the probability distribution of the shadowing time contains two distinct scaling behaviors: an algebraic scaling for short times and an exponential scaling for long times. The exponential behavior depends on the system details but the small-time algebraic behavior appears to be universal.
authors.affiliation: Department of Mathematics and Statistics, Arizona State University, Tempe 85287, USA.
authors.forename: Younghae
authors.initials: Y
authors.lastname: Do
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
authors.forename: Zonghua
authors.initials: Z
authors.lastname: Liu
authors.forename: Eric J
authors.initials: EJ
authors.lastname: Kostelich