In [4], we have studied the statistical properties and mono-fractality of the power system time series, voltage magnitude (V), frequency (f), and phase angle (θ). The power system data was measured using three Phasor Measurement Units (PMUs) installed at Baylor University, Harris Substation, McDonald Observatory in the Texas Synchrophasor Network [1]. Our analysis of several data sets has shown...

Local expansion exponents for nonequilibrium dynamical systems, described by partial differential equations, are introduced. These exponents show whether the system phase volume expands, contracts, or is conserved in time. The ways of calculating the exponents are discussed. The principle of minimal expansion provides the basis for treating the problem of pattern selection. The exponents are al...

We show that the change of fluctuation spectrum near quantum critical point (QCP) may result in continuous exponents with temperature due to increase effective dimensionality upon approach QCP. The latter reflects crossover from thermal fluctuations white noise mode regime. investigate dynamics an exemplary system obeying Bose–Einstein employing Keldysh–Schwinger and develop renormalization gro...

<p style='text-indent:20px;'>We study circle maps with a flat interval where the critical exponents at two boundary points of spot might be different. The space such systems is partitioned in connected parts whose common only depends on exponents. At this there phase transition geometry system. Differently from previous approaches, achieved by studying asymptotical behavior renormalizatio...

Let $F$ be a non-Archimedean locally compact field‎. ‎Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$‎. ‎We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$‎. ‎We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$‎. ‎Using the Langlands...

Many systems in the natural world exhibit chaos or non-linear behavior, the complexity of which is so great that they appear to be random. Identification of chaos in experimental data is essential for characterizing the system and for analyzing the predictability of the data under analysis. The Lyapunov exponents provide a quantitative measure of the sensitivity to initial conditions and are th...

Inasmuch as Lyapunov exponents provide a necessary condition for chaos in a dynamical system, confidence bounds on estimated Lyapunov exponents are of great interest. Estimates derived either from observations or from numerical integrations are limited to trajectories of finite length, and it is the uncertainties in (the distribution of) these finite time Lyapunov exponents which are of interes...