Estimating the Dimension of an Inertial Manifold from Unstable Periodic Orbits

X. Ding (1) , H. Chate (2) , P. Cvitanović (1) , E. Siminos (3) , K.A. Takeuchi (4)

1 CNS-GATECH - Center for Nonlinear Science
2 SPHYNX - Systèmes Physiques Hors-équilibre, hYdrodynamique, éNergie et compleXes
3 Chalmers University of Technology, Department of Applied Physics, Division of Nuclear Engineering, SE-412 96 Göteborg, Sweden
4 Department of Applied Physics, The University of Tokyo

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.

Domains: Physics [physics]

X. Ding, H. Chate, P. Cvitanović, E. Siminos, K.A. Takeuchi. Estimating the Dimension of an Inertial Manifold from Unstable Periodic Orbits. Physical Review Letters, 2016, 117, pp.024101. ⟨10.1103/PhysRevLett.117.024101⟩. ⟨cea-01483878⟩