Estimating the Dimension of an Inertial Manifold from Unstable Periodic Orbits

X. Ding; H. Chate; P. Cvitanović; E. Siminos; K.A. Takeuchi

doi:10.1103/PhysRevLett.117.024101

Journal articles

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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Journal articles

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Physics [physics]

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