Lower estimates of top Lyapunov exponent for cooperative random systems of linear ODEs

On Lipschitz Continuity of the Top Lyapunov Exponent of Linear Parameter Varying and Linear Switching Systems

We study families of time-varying linear systems, where time-variations have to satisfy restrictions on the dwell time, that is, on the minimum distance between discontinuities, as well as on the derivative in between discontinuities. For this class of systems we study continuity properties of the growth rate as a function of the systems’ data. It is shown by example, that a straightforward top...

Lyapunov Exponent for Products of Random Matrices

Anomalous convergence of Lyapunov exponent estimates.

Numerical experiments reveal that estimates of the Lyapunov exponent for the logistic map x t+1 = f(x t) = 4x t (1 ? x t) are anomalously precise: they are distributed with a standard deviation that scales as 1=N, where N is the length of the trajectory, not as 1= p N, the scaling expected from an informal interpretation of the central limit theorem. We show that this anomalous convergence foll...

Semi-analytic estimates of Lyapunov exponents in lower-dimensional systems

Statistical arguments, seemingly well-justified in higher dimensions, can also be used to derive reasonable estimates of Lyapunov exponents χ in lower-dimensional Hamiltonian systems. This Letter explores the assumptions incorporated into these arguments. The predicted χ’s are insensitive to most details, but do depend sensitively on the nongeneric form of the auto-correlation function characte...

Positive Lyapunov Exponent by a Random Perturbation

We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood. We provide conditions under which the perturbed system is ergodic and admits a positive Lyapunov exponent, with an explicit lower bound, for a large and controlled set of parameter values. Acknowledgements. The authors are indebted to Lai-S...