Lyapunov Exponent for Whitney’s Problem with Random Drive

Lyapunov Exponent for Products of Random Matrices

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...

Exact Lyapunov Exponent for Infinite Products of Random Matrices

In this work, we give a rigorous explicit formula for the Lyapunov exponent for some binary infinite products of random 2 × 2 real matrices. All these products are constructed using only two types of matrices, A and B, which are chosen according to a stochastic process. The matrix A is singular, namely its determinant is zero. This formula is derived by using a particular decomposition for the ...

Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, λ and λ respectively. We discuss the numerical difficulties that arise in the numerical calculation of λ in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically λ by using a cumulant ...

Evaluating Lyapunov exponent spectra with neural networks

A method using discrete cross-correlation for identifying and removing spurious Lyapunov exponents when embedding experimen tal data in a dimension greater than the origina l system is introduce d. The method uses a distribution of calculated exponent values produced by modeling a single time series many times or multiple instances of a time series. For this task, global models are shown to com...