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arXiv · 1604.01859

Estimating dimension of inertial manifold from unstable periodic orbits

X. Ding·H. Chaté·P. Cvitanović·E. Siminos·K. A. Takeuchi
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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 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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X. Ding, H. Chaté, P. Cvitanović, E. Siminos, K. A. Takeuchi. 2016-04-07. Estimating dimension of inertial manifold from unstable periodic orbits. https://doi.org/10.1103/physrevlett.117.024101

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