Positive Characteristic Exponents Research Articles

Sushchestvovanie antiperronovskogo effekta smeny polozhitel'nykh pokazateley sistemy lineynogo priblizheniya na otritsatel'nye pri vozmushcheniyakh vysshego poryadka malosti

We prove the existence of a two-dimensional linear system x˙ = A(t)x, t ≥ t0, withbounded infinitely differentiable coefficients and all positive characteristic exponents, as wellas an infinitely differentiable m-perturbation f(t, y) having an order m 1 of smallness ina neighborhood of the origin y = 0 and an order of growth not exceeding m outside it, such thatthe perturbed system y˙ = A(t)y + f(t, y), y ∈ R2, t ≥ t0, has a solution y(t) with a negativeLyapunov exponent.

Linear Version of the Anti-Perron Effect of Change of Positive Characteristic Exponents to Negative Ones

Linear Version of the Anti-Perron Effect of Change of Positive Characteristic Exponents to Negative Ones

On the Existence of Linear Differential Systems with All Positive Characteristic Exponents of the First Approximation and with Exponentially Decaying Perturbations and Solutions

On the Existence of Linear Differential Systems with All Positive Characteristic Exponents of the First Approximation and with Exponentially Decaying Perturbations and Solutions

Construction of an Arbitrary Suslin Set of Positive Characteristic Exponents in the Perron Effect

For an arbitrary bounded Suslin set S ⊂ (0, +∞) and arbitrary parameters m > 1 and λ1 ≤ λ2 1 in a neighborhood of the origin y = 0 and of an admissible order of growth outside it: ‖ f (t,y)‖ ≤ const ‖y‖m, y ∈ ℝ2, t ⁥ t0.

DC Flashover Performance of Ice-Covered Composite Insulators with Parallel Air Gaps

DC flashover performance of ice-covered composite insulators with a parallel air gap (CI/PAG) is an important technical consideration when such insulators are used to isolate ground wires for the purpose of DC ice-melting. Tests on tension and suspension types of CI/PAG were thus carried out in the artificial climate chamber to investigate their DC icing flashover performance. The influences of parallel air gap, ice thickness, pollution severity and air pressure on DC negative 50% flashover voltage (U50%) of CI/PAG were investigated. Test results show that the parallel air gap affected both the discharge path and U50%. With increasing ice thickness, U50% declined by up to 52%; this effect was more evident when the breakdown occurred in the air gap. The pollution severity affected U50% only when the flashover happened along insulator surface. With a decrease of atmospheric pressure, U50% decreased. U50% and the ratio of air pressure were in a power function relationship with a positive characteristic exponent which was relevant to the discharge path.

On the perron sign change effect for Lyapunov characteristic exponents of solutions of differential systems

The Perron effect is the effect in which the characteristic Lyapunov exponents of solutions of a differential system change sign from negative to positive when passing to a perturbed system. We show that this effect is realized on all nontrivial solutions of two two-dimensional systems: an original linear system with negative characteristic exponents and a perturbed system with small perturbations of arbitrary order m > 1 in a neighborhood of the origin, all of whose nontrivial solutions have positive characteristic exponents. We compute the exact positive value of the characteristic exponents of solutions of the two-dimensional nonlinear Perron system with small second-order perturbations, which realizes only a partial Perron effect.

Detection of chaotic determinism in time series from randomly forced maps

Time series from biological systems often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely “noise”. Despite this effort, it has been difficult to establish the presence of chaos in time series from biological systems. The output from a biological system is probably the result of both its internal dynamics, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Local dimension for piecewise monotonic maps on the interval

AbstractThe local dimension of invariant and conformal measures for piecewise monotonic transformations on the interval is considered. For ergodic invariant measures m with positive characteristic exponent χm we show that the local dimension exists almost everywhere and equals hm/χm For certain conformal measures we show a relation between a pressure function and the Hausdorff dimension of sets, on which the local dimension is constant.

Absence of sensitivity to initial conditions in quantum dynamics.

A canonical generalization of the notion of sensitivity to initial conditions is developed for quantum dynamics and used to define the spectrum of characteristic exponents for quantum systems. It is then shown, under very general conditions, that there exists no positive characteristic exponent nor any sensitivity to initial conditions, however weak, in quantum dynamics. This result implies the nonexistence of chaos is quantum mechanics.