Estimating dimension of inertial manifold from unstable periodic orbits
Journal article, 2016
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.