title: Shadowability of statistical averages in chaotic systems.
abstract: We ask whether statistical averages in chaotic systems can be computed or measured reliably under the influence of noise. Situations are identified where the invariance of such averages breaks down as the noise amplitude increases through a critical level. An algebraic scaling law is obtained which relates the change of the averages to the noise variation. This breakdown of shadowability of statistical averages, as characterized by the algebraic scaling law, can be expected in both low- and high-dimensional chaotic systems.
authors.affiliation: Department of Mathematics and Center for Systems Science and Engineering Research, Arizona State University, Tempe, Arizona 85287, USA.
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
authors.forename: Zonghua
authors.initials: Z
authors.lastname: Liu
authors.forename: Guo-Wei
authors.initials: GW
authors.lastname: Wei
authors.forename: Choy-Heng
authors.initials: CH
authors.lastname: Lai