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.

Document type :

Journal articles

Domain :

Physics [physics]

Complete list of metadata

https://hal-cea.archives-ouvertes.fr/cea-01483878
Contributor : Dominique Girard Connect in order to contact the contributor
Submitted on : Monday, March 6, 2017 - 3:34:22 PM
Last modification on : Monday, December 13, 2021 - 9:16:32 AM
Long-term archiving on: : Wednesday, June 7, 2017 - 2:35:14 PM

PhysRevLett.117.024101.pdf

Publisher files allowed on an open archive

Estimating the Dimension of an Inertial Manifold from Unstable Periodic Orbits

File

Identifiers

Collections

Citation

Export

Metrics

Estimating the Dimension of an Inertial Manifold from Unstable Periodic Orbits

File

Identifiers

Collections

Citation

Export

Share

Metrics