Covariant Lyapunov vectors

Francesco Ginelli, Hugues Chaté, Roberto Livi, Antonio Politi

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here, we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets' theorem for the properties of the CLVs. We then present a detailed description of a 'dynamical' algorithm to compute the CLVs and show that it generically converges exponentially in time. We also discuss its numerical performance and compare it with other algorithms presented in the literature. We finally illustrate how CLVs can be used to quantify deviations from hyperbolicity with reference to a dissipative system (a chain of Hénon maps) and a Hamiltonian model (a Fermi-Pasta-Ulam chain). This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Lyapunov analysis: from dynamical systems theory to applications'.
Original languageEnglish
Article number254005
Number of pages25
JournalJournal of Physics. A, Mathematical and theoretical
Volume46
Issue number25
Early online date4 Jun 2013
DOIs
Publication statusPublished - 28 Jun 2013

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Lyapunov
Hamiltonians
Chaotic systems
System theory
Ergodic Theory
dynamical systems
Dissipative Systems
Hyperbolicity
Dynamical systems
Systems Theory
Physics
theorems
Chaotic System
Phase Space
deviation
Quantify
Deviation
Dynamical system
physics
Converge

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Covariant Lyapunov vectors. / Ginelli, Francesco; Chaté, Hugues; Livi, Roberto; Politi, Antonio.

In: Journal of Physics. A, Mathematical and theoretical, Vol. 46, No. 25, 254005, 28.06.2013.

Research output: Contribution to journalArticle

Ginelli, Francesco ; Chaté, Hugues ; Livi, Roberto ; Politi, Antonio. / Covariant Lyapunov vectors. In: Journal of Physics. A, Mathematical and theoretical. 2013 ; Vol. 46, No. 25.
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