Lyapunov Exponent Testing for AWGN Generator System

Reflecting on the AWGN Error Exponent

Recently it was shown that a lattice code with lattice decoding can achieve the capacity of the additive white Gaussian noise (AWGN) channel. This was achieved by using a minimum mean-square error (MMSE) scaling and dithering to transform the AWGN channel into a modulo-lattice additive noise (mod-Λ) channel. Further, Liu et. al. have shown that lattice decoding can achieve the error exponent of...

Lyapunov Exponent for Products of Random Matrices

Maximal Lyapunov exponent at crises.

We study the variation of Lyapunov exponents of simple dynamical systems near attractor-widening and attractor-merging crises. The largest Lyapunov exponent has universal behaviour, showing abrupt variation as a function of the control parameter as the system passes through the crisis point, either in the value itself, in the case of the attractor-widening crisis, or in the slope, for attractor...

Discontinuity of the Lyapunov Exponent

We study discontinuity of the Lyapunov exponent. We construct a limit-periodic Schrödinger operator, of which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials, whose Lyapunov exponent is discontinuous, are dense in the space of limit-periodic potentials.

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...