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 the Kuramoto-Sivashinsky system and find it to be equal to the “physical dimension” computed previously via the hyperbolicity properties of covariant Lyapunov vectors.
- Received 28 April 2016
DOI:https://doi.org/10.1103/PhysRevLett.117.024101
© 2016 American Physical Society