Characterizing Dynamics with Covariant Lyapunov Vectors
Abstract
A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows us to address fundamental questions such as the degree of hyperbolicity, which can be quantified in terms of the transversality of these intrinsic vectors. For spatially extended systems, the covariant Lyapunov vectors have localization properties and spatial Fourier spectra qualitatively different from those composing the orthonormalized basis obtained in the standard procedure used to calculate the Lyapunov exponents.
- Publication:
-
Physical Review Letters
- Pub Date:
- September 2007
- DOI:
- arXiv:
- arXiv:0706.0510
- Bibcode:
- 2007PhRvL..99m0601G
- Keywords:
-
- 05.70.Ln;
- 05.90.+m;
- 45.70.-n;
- 87.18.Ed;
- Nonequilibrium and irreversible thermodynamics;
- Other topics in statistical physics thermodynamics and nonlinear dynamical systems;
- Granular systems;
- Aggregation and other collective behavior of motile cells;
- Nonlinear Sciences - Chaotic Dynamics;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 4 pages, 3 figures, submitted to Physical Review letters