Estimating dimension of inertial manifold from unstable periodic orbits
Chaotic Dynamics
2016-07-13 v1
Abstract
We provide numerical evidence that a finite-dimensional inertial manifold on which the dynamics of a chaotic dissipative dynamical system lives can be constructed solely from the knowledge of a set of unstable periodic orbits. In particular, we determine the dimension of the inertial manifold for Kuramoto-Sivashinsky system, and find it to be equal to the `physical dimension' computed previously via the hyperbolicity properties of covariant Lyapunov vectors.
Keywords
Cite
@article{arxiv.1604.01859,
title = {Estimating dimension of inertial manifold from unstable periodic orbits},
author = {X. Ding and H. Chaté and P. Cvitanović and E. Siminos and K. A. Takeuchi},
journal= {arXiv preprint arXiv:1604.01859},
year = {2016}
}
Comments
6 pages, 3 pdf figures, uses revtex4