Local characterization of transient chaos on finite times in open systems
Abstract
To characterize local finite-time properties associated with transient chaos in open dynamical systems, we introduce an escape rate and fractal dimensions suitable for this purpose in a coarse-grained description. We numerically illustrate that these quantifiers have a considerable spread across the domain of the dynamics, but their spatial variation, especially on long but non-asymptotic integration times, is approximately consistent with the relationship that was recognized by Kantz and Grassberger for temporally asymptotic quantifiers. In particular, deviations from this relationship are smaller than differences between various locations, which confirms the existence of such a dynamical law and the suitability of our quantifiers to represent underlying dynamical properties in the non-asymptotic regime.
Keywords
Cite
@article{arxiv.2011.02283,
title = {Local characterization of transient chaos on finite times in open systems},
author = {Gábor Drótos and Emilio Hernández-García and Cristóbal López},
journal= {arXiv preprint arXiv:2011.02283},
year = {2021}
}
Comments
23 pages, 8 figures. Revision based on referee reports: minor corrections and a new analysis of the deviation from the Kantz-Grassberger relationship