Scrambling of information in a quantum many-body system, quantified by the out-of-time-ordered correlator (OTOC), is key manifestation chaos. A regime exponential growth OTOC, characterized Lyapunov exponent, has so far mostly been observed systems with high-dimensional local Hilbert space and weakly-coupled systems. Here, we propose general criterion for existence well-defined OTOC spatially e...

In this article, we consider the ergodic optimization of top Lyapunov exponent. We prove that there is a unique maximising measure exponent for typical matrix cocyles. By using results obtain, in any nonuniquely minimal dynamical system, Lyapunov-irregular points are

We prove that for any holomorphic map, and bounded orbit which does not accumulate to a singular set or an attracting cycle, its lower Lyapunov exponent is non-negative. The same result holds unbounded orbits, maps with set. Furthermore, the may infinity set, as long it slow enough.

We discuss several bifurcation phenomena that occur in the quasiperiodically driven logistic map. This system can have strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors; on SNAs the dynamics is aperiodic, but the largest Lyapunov exponent is nonpositive. There are a number of different transitions that occur here, from periodic attractors to SNAs, from SNAs to c...

The classical motion of a Ii"ee particle that scatters elastically from ring-bounded cavities is analyzed nunaerically. When the ring is a smooth circle the scattering follows a regular and periodic pattern. However, for rings composed of N scatrefers the Ilow is irregular, of Lyapunov type. The Lyapunov exponent is found to depend logarithmically with N, which is consistent with the theoretica...

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...