We show the sum of the first k Lyapunov exponents of linear cocycles is an upper semicontinuous function in the L topologies, for any 1 ≤ p ≤ ∞ and k. This fact, together with a result from Arnold and Cong, implies that the Lyapunov exponents of the L-generic cocycle, p < ∞, are all equal.

An efficient and numerically stable method to determine all the Lyapunov characteristic exponents of a dynamical system is developed. Numerical experiments are presented highlighting some aspects of convergence, accuracy and efficiency in the computation of the Lyapunov characteristic exponents. PACS Codes: 05.45.+b, 02.70.-C

Constraints are found on the spatial variation of finite-time Lyapunov exponents of two- and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of separation, along characteristic directions, of neighboring trajectories. The solution of the equations is a coordinate transformation that takes initial conditi...

In this paper we describe the maximal and the minimal values of Lyapunov exponents for second order discrete time invariant linear system perturbed by time varying bounded perturbation. The results may be interpreted in terms of generalized spectral radius and applied to obtained formulas for robust stability problem. Key-Words: Time varying discrete linear systems, Lyapunov exponents, robust s...

We describe a simple continuous-time flow such that Lyapunov exponents fail to exist at nearly every point in the phase space R2 , despite the fact that the flow admits a unique natural measure. This example illustrates that the existence of Lyapunov exponents is a subtle question for systems that are not conservative.

In this paper, we consider discrete and continuous QR algorithms for computing all of the Lyapunov exponents of a regular dynamical system. We begin by reviewing theoretical results for regular systems and present general perturbation results for Lyapunov exponents. We then present the algorithms, give an error analysis of them, and describe their implementation. Finally, we give several numeri...

We generalize the concept of Lyapunov exponent to transformations that are not necessarily differentiable. For fairly large classes of repellers and of hyperbolic sets of differentiable maps, the new exponents are shown to coincide with the classical ones. We also discuss the relation of the new Lyapunov exponents with the dimension theory of dynamical systems for invariant sets of continuous t...

Lyapunov exponents of a dynamical system give information about its long-term evolution. Exponents estimation is not an easy task; it is computationally costly and, in presence of chaotic dynamics, it exhibits numerical difficulties. In a previous paper, the authors proposed an algorithm for Lyapunov exponents estimation in piecewise linear systems that strongly reduces the computational time. ...

Boundary effects in the stepwise structure of the Lyapunov spectra and corresponding wavelike structure of the Lyapunov vectors are discussed numerically in quasi-one-dimensional systems of many hard disks. Four different types of boundary conditions are constructed by combinations of periodic boundary conditions and hard-wall boundary conditions, and each leads to different stepwise structures...

in this paper, we introduce a new hyperchaotic complex t-system. this system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. we discuss the synchronization with certain and uncerta...