TY - JOUR
T1 - Covariant Lyapunov vectors
AU - Ginelli, Francesco
AU - Chaté, Hugues
AU - Livi, Roberto
AU - Politi, Antonio
PY - 2013/6/28
Y1 - 2013/6/28
N2 - 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'.
AB - 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'.
UR - http://www.scopus.com/inward/record.url?scp=84878778426&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/46/25/254005
DO - 10.1088/1751-8113/46/25/254005
M3 - Article
AN - SCOPUS:84878778426
SN - 1751-8113
VL - 46
JO - Journal of Physics. A, Mathematical and theoretical
JF - Journal of Physics. A, Mathematical and theoretical
IS - 25
M1 - 254005
ER -