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Journal Articles Journal of Physics A: Mathematical and Theoretical Year : 2013

Covariant Lyapunov vectors

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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).

Dates and versions

cea-01478874 , version 1 (28-02-2017)

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Cite

Francesco Ginelli, Hugues Chaté, Roberto Livi, Antonio Politi. Covariant Lyapunov vectors. Journal of Physics A: Mathematical and Theoretical, 2013, 46 (25), ⟨10.1088/1751-8113/46/25/254005⟩. ⟨cea-01478874⟩
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