title: Estimating the Dimension of an Inertial Manifold from Unstable Periodic Orbits.
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.
authors.affiliation: Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA.
authors.forename: X
authors.initials: X
authors.lastname: Ding
authors.affiliation: Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette, France.|Beijing Computational Science Research Center, Beijing 100094, China.
authors.forename: H
authors.initials: H
authors.lastname: Chaté
authors.affiliation: Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA.
authors.forename: P
authors.initials: P
authors.lastname: Cvitanović
authors.affiliation: Department of Physics, Chalmers University of Technology, Gothenburg SE-412 96, Sweden.
authors.forename: E
authors.initials: E
authors.lastname: Siminos
authors.affiliation: Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan.
authors.forename: K A
authors.initials: KA
authors.lastname: Takeuchi