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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
SPEC - UMR3680 - Service de physique de l'état condensé, IRAMIS - Institut Rayonnement Matière de Saclay
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
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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https://hal-cea.archives-ouvertes.fr/cea-01483878
Contributor : Dominique Girard <>
Submitted on : Monday, March 6, 2017 - 3:34:22 PM
Last modification on : Monday, February 10, 2020 - 6:14:06 PM
Long-term archiving on: : Wednesday, June 7, 2017 - 2:35:14 PM

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CEA | CNRS | DSM-IRAMIS | IRAMIS-SPEC | UNIV-PARIS-SACLAY | CEA-DRF | CEA-UPSAY

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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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