On sensitive dependence on initial conditions and existence of physical measure for 3-flows
Dynamical Systems
2014-03-14 v3
Abstract
After reviewing known results on sensitiveness and also on robustness of attractors together with observations on their proofs, we show that for attractors of three-dimensional flows, robust chaotic behavior meaning sensitiveness to initial conditions for the past as well for the future for all nearby flows) is equivalent to the existence of certain hyperbolic structures. These structures, in turn, are associated to the existence of physical measures. In short in low dimensions, robust chaotic behavior for smooth flows ensures the existence of a physical measure.
Keywords
Cite
@article{arxiv.0804.3616,
title = {On sensitive dependence on initial conditions and existence of physical measure for 3-flows},
author = {Vitor Araujo},
journal= {arXiv preprint arXiv:0804.3616},
year = {2014}
}
Comments
18 pages; 6 figures. To: Modelling, Optimization and BioEconomy, Eds. Alberto Pinto and David Zilberman. arXiv admin note: substantial text overlap with arXiv:math/0403273