Measurable Time-Restricted Sensitivity
Dynamical Systems
2014-01-23 v1
Abstract
We develop two notions of time-restricted sensitivity to initial conditions for measurable dynamical systems, where the time before divergence of a pair of paths is at most an asymptotically logarithmic function of a measure of their initial distance. In the context of finite measure-preserving transformations on a compact space, we relate these notions to the metric entropy of the system. We examine one of these notions for classes of non-measure-preserving, nonsingular transformations.
Cite
@article{arxiv.1105.1493,
title = {Measurable Time-Restricted Sensitivity},
author = {Domenico Aiello and Hansheng Diao and Zhou Fan and Daniel O. King and Jessica Lin and Cesar E. Silva},
journal= {arXiv preprint arXiv:1105.1493},
year = {2014}
}