http://www.cnr.it/ontology/cnr/individuo/prodotto/ID202928

Hyperbolic decoupling of tangent space and effective dimension of dissipative systems (Articolo in rivista)

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Hyperbolic decoupling of tangent space and effective dimension of dissipative systems (Articolo in rivista) (literal)

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Alternative label

Kazumasa A. Takeuchi (1,2); Hong-liu Yang (3); Francesco Ginelli (1,4,5,6); Günter Radons (3); Hugues Chaté (1) (2011)
Hyperbolic decoupling of tangent space and effective dimension of dissipative systems
in Physical review. E, Statistical, nonlinear, and soft matter physics (Print)
(literal)

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Kazumasa A. Takeuchi (1,2); Hong-liu Yang (3); Francesco Ginelli (1,4,5,6); Günter Radons (3); Hugues Chaté (1) (literal)

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1) Service de Physique de l'État Condensé, CEA-Saclay, F-91191 Gif-sur-Yvette, France 2) Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 3) Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany 4) Istituto dei Sistemi Complessi (ISC), CNR, Via dei Taurini 19, I-00185 Roma, Italy 5) Physics Department, University of Florence, Via Sansone 1, I-50019 Sesto Fiorentino, Italy 6) Department of Physics and SUPA, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom (literal)

Titolo

Hyperbolic decoupling of tangent space and effective dimension of dissipative systems (literal)

Abstract

We show, using covariant Lyapunov vectors, that the tangent space of spatially extended dissipative systems is split into two hyperbolically decoupled subspaces: one comprising a finite number of frequently entangled \"physical\" modes, which carry the physically relevant information of the trajectory, and a residual set of strongly decaying \"spurious\" modes. The decoupling of the physical and spurious subspaces is defined by the absence of tangencies between them and found to take place generally; we find evidence in partial differential equations in one and two spatial dimensions and even in lattices of coupled maps or oscillators. We conjecture that the physical modes may constitute a local linear description of the inertial manifold at any point in the global attractor. (literal)

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