Uncertainty Relation for Chaos
Mathematical Physics
2015-06-15 v1 math.MP
Chaotic Dynamics
Abstract
A necessary condition for the emergence of chaos is given. It is well known that the emergence of chaos requires a positive exponent which entails diverging trajectories. Here we show that this is not enough. An additional necessary condition for the emergence of chaos in the region where the trajectory of the system goes through, is that the product of the maximal positive exponent times the duration in which the system configuration point stays in the unstable region should exceed unity. We give a theoretical analysis justifying this result and a few examples.
Keywords
Cite
@article{arxiv.1112.2101,
title = {Uncertainty Relation for Chaos},
author = {A. Yahalom and M. Lewkowicz and J. Levitan and G. Elgressy and L. P. Horwitz and Y. Ben-Zion},
journal= {arXiv preprint arXiv:1112.2101},
year = {2015}
}
Comments
5 pages, 6 figures