English

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