Related papers: Computing covariant Lyapunov vectors in Hilbert sp…
The recent years have witnessed a growing interest for 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…
Linear perturbations of solutions of dynamical systems exhibit different asymptotic growth rates, which are naturally characterized by so-called covariant Lyapunov vectors (CLVs). Due to an increased interest of CLVs in applications,…
In this thesis, we review the theory of Lyapunov exponents and covariant Lyapunov vectors (CLVs) and use these objects to numerically investigate the dynamics of several autonomous Hamiltonian systems. The algorithm which we use for…
Dynamical vectors characterizing instability and applicable as ensemble perturbations for prediction with geophysical fluid dynamical models are analysed. The relationships between covariant Lyapunov vectors (CLVs), orthonormal Lyapunov…
Covariant Lyapunov vectors (CLVs) are useful in multiple applications, but the optimal time windows needed to accurately compute these vectors are yet unclear. To remedy this, we investigate two methods for determining when to safely…
Covariant Lyapunov vectors or CLVs span the expanding and contracting directions of perturbations along trajectories in a chaotic dynamical system. Due to efficient algorithms to compute them that only utilize trajectory information, they…
We carry out extensive computer simulations to study the Lyapunov instability of a two-dimensional hard disk system in a rectangular box with periodic boundary conditions. The system is large enough to allow the formation of Lyapunov modes…
We apply to bidimensional chaotic maps the numerical method proposed by Ginelli et al. to approximate the associated Oseledets splitting, i.e. the set of linear subspaces spanned by the so called covariant Lyapunov vectors (CLV) and…
Covariant vectors, Lyapunov vectors, or Oseledets vectors are increasingly being used for a variety of model analyses in areas such as partial differential equations, nonautonomous differentiable dynamical systems, and random dynamical…
Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate…
A new method to describe hyperbolic patterns in two dimensional flows is proposed. The method is based on the Covariant Lyapunov Vectors (CLVs), which have the properties to be covariant with the dynamics, and thus being mapped by the…
We study a simplified coupled atmosphere-ocean model using the formalism of covariant Lyapunov vectors (CLVs), which link physically-based directions of perturbations to growth/decay rates. The model is obtained via a severe truncation of…
Two sets of vectors, covariant and orthogonal Lyapunov vectors (CLVs/OLVs), are currently used to characterize the linear stability of chaotic systems. A comparison is made to show their similarity and difference, especially with respect to…
The classical approach for studying atmospheric variability is based on defining a background state and studying the linear stability of the small fluctuations around such a state. Weakly non-linear theories can be constructed using higher…
We explore the high dimensional chaos of a one-dimensional lattice of diffusively coupled tent maps using the covariant Lyapunov vectors (CLVs). We investigate the connection between the dynamics of the maps in the physical space and the…
A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows to address fundamental questions such as the degree of hyperbolicity, which can be quantified in…
Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a number of simple models,…
While a previously proposed method for estimating inertial manifold dimension, based on explicitly computing angles between pairs of covariant Lyapunov vectors (CLVs), employs efficient algorithms, it remains computationally demanding due…
In order to analyze structure of tangent spaces of a transient orbit, we propose a new algorithm which pulls back vectors in tangent spaces along the orbit by using a calculation method of covariant Lyapunov vectors. As an example, the…
We explore the chaotic dynamics of a large one-dimensional lattice of coupled maps with diffusive coupling of varying strength using the covariant Lyapunov vectors (CLVs). Using a lattice of diffusively coupled quadratic maps we quantify…