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Estimating the Dimension of an Inertial Manifold from Unstable Periodic Orbits

Authors :: Ding, X.
Chate, H.
Cvitanovic, P.
Siminos, E.
Takeuchi, Kazumasa
Center for Nonlinear Science (CNS-GATECH)
Georgia Institute of Technology [Atlanta]
Systèmes Physiques Hors-équilibre, hYdrodynamique, éNergie et compleXes (SPHYNX)
Service de physique de l'état condensé (SPEC - UMR3680)
Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut Rayonnement Matière de Saclay (IRAMIS)
Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay
Chalmers University of Technology, Department of Applied Physics, Division of Nuclear Engineering, SE-412 96 Göteborg, Sweden
Department of Applied Physics, The University of Tokyo
The University of Tokyo (UTokyo)
The National Science Foundation under Grants Nos. DMS- 1211827 and CMMI-1028133. JSPS KAKENHI Grant Nos. JP25707033 and JP25103004, as well as the JSPS Core-to-CoreProgram 'Non-equilibrium dynamics of soft matter and information'.
Source :: Physical Review Letters, Physical Review Letters, American Physical Society, 2016, 117, pp.024101. ⟨10.1103/PhysRevLett.117.024101⟩, Physical Review Letters, 2016, 117, pp.024101. ⟨10.1103/PhysRevLett.117.024101⟩
Publication Year :: 2016
Publisher :: HAL CCSD, 2016.
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.<br />Comment: 6 pages, 3 pdf figures, uses revtex4

Details

Language :: English
ISSN :: 00319007 and 10797114
Database :: OpenAIRE
Journal :: Physical Review Letters, Physical Review Letters, American Physical Society, 2016, 117, pp.024101. ⟨10.1103/PhysRevLett.117.024101⟩, Physical Review Letters, 2016, 117, pp.024101. ⟨10.1103/PhysRevLett.117.024101⟩
Accession number :: edsair.doi.dedup.....12a65bb6b9a884b84cc50d65d37e04df
Full Text :: https://doi.org/10.1103/PhysRevLett.117.024101⟩