Scaling Laws for Shadowing Time

Thursday, November 20, 1997 - 11:00am - 12:00pm
Keller 3-180
Timothy Sauer (George Mason University)
A shadowing trajectory is a true trajectory of a map or differential equation, that closely tracks a computed approximate solution. For systems exhibiting hyperbolic and near-hyperbolic chaos, long shadowing trajectories can be shown to exist, meaning that trajectories constructed in the presence of one-step errors still represent true system behavior. We will report on recent studies of strongly nonhyperbolic systems, in the case where finite-time Lyapunov exponents fluctuate about zero, for which long shadowing trajectories apparently do not exist. Scaling laws govern the length of shadowing trajectories in terms of one-step error and the statistics of the finite-time Lyapunov exponents.