Estimating dimension of inertial manifold from unstable periodic orbits
  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. 
X. Ding, H. Chat\'e, P. Cvitanovi\'c, E. Siminos, K. A. Takeuchi
nlin.CD