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.
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Physical Review Letters, American Physical Society, 2016, 117, pp.024101. 〈10.1103/PhysRevLett.117.024101〉
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PhysRevLett.117.024101.pdf
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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, American Physical Society, 2016, 117, pp.024101. 〈10.1103/PhysRevLett.117.024101〉. 〈cea-01483878〉

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