%0 Book Section %1 statphys23_0512 %A Ginelli, F. %A Chate, H. %A Livi, R. %A Poggi, P. %A Politi, A. %A Turchi, A. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K hyperbolicity localization lyapunov oseledec space splitting statphys23 tangent topic-5 vectors %T Characterizing dynamics through covariant Lyapunov vectors %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=512 %X We introduce a general, innovative approach to determine, in both continuous- and discrete-time dynamical systems, an intrinsic set of directions at each point of phase space that are covariant with the dynamics as well as invariant under time reversal. We argue that, for any invertible dynamical system, the intrinsic tangent space decomposition introduced by these directions - the covariant Lyapunov vectors (CLV) - coincides with the so called Oseledec splitting. The knowledge of CLV allows for a more accurate characterization of the underlying dynamics. In particular, it is possible to quantify a general property such as the degree of hyperbolicity or to compute the complete spectrum of Lyapunov exponents via ensemble averages over the attractor invariant measure rather than through time averages. Moreover, statistical properties of CLV differ from those of the vectors obtained from the standard orthogonalization procedure introduced by Benettin et al. In particular, we show evidence in both dissipative and Hamiltonian spatially extended systems that CLV are strictly localized almost everywhere in the asymptotic spectrum, thus providing a meaningful hierarchical decomposition of spatiotemporal chaos.

@incollection{statphys23_0512, abstract = {We introduce a general, innovative approach to determine, in both continuous- and discrete-time dynamical systems, an intrinsic set of directions at each point of phase space that are covariant with the dynamics as well as invariant under time reversal. We argue that, for any invertible dynamical system, the intrinsic tangent space decomposition introduced by these directions - the {\it covariant} Lyapunov vectors (CLV) - coincides with the so called Oseledec splitting. The knowledge of CLV allows for a more accurate characterization of the underlying dynamics. In particular, it is possible to quantify a general property such as the degree of hyperbolicity or to compute the complete spectrum of Lyapunov exponents via ensemble averages over the attractor invariant measure rather than through time averages. Moreover, statistical properties of CLV differ from those of the vectors obtained from the standard orthogonalization procedure introduced by Benettin et al. In particular, we show evidence in both dissipative and Hamiltonian spatially extended systems that CLV are strictly localized almost everywhere in the asymptotic spectrum, thus providing a meaningful hierarchical decomposition of spatiotemporal chaos.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Ginelli, F. and Chate, H. and Livi, R. and Poggi, P. and Politi, A. and Turchi, A.}, biburl = {https://www.bibsonomy.org/bibtex/2756f6e41c91b7ae36818020ede0fb4ee/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {0f882c8057e267dbe46ef83224a19f4d}, intrahash = {756f6e41c91b7ae36818020ede0fb4ee}, keywords = {hyperbolicity localization lyapunov oseledec space splitting statphys23 tangent topic-5 vectors}, month = {9-13 July}, timestamp = {2007-06-20T10:16:22.000+0200}, title = {Characterizing dynamics through covariant Lyapunov vectors}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=512}, year = 2007 }