Positive Lyapunov Exponent by a Random Perturbation
نویسندگان
چکیده
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-Sang Young for stimulating discussions. Mikko Stenlund has received funding from the Academy of Finland.
منابع مشابه
Perturbative test of single parameter scaling for 1D random media
Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance is equal to the Lyapunov exponent. We settle discussions about its validity for a wide class of models by proving that, away from anomalies, single paramete...
متن کاملRandom Logistic Maps and Lyapunov Exponents
We prove that under certain basic regularity conditions, a random iteration of logistic maps converges to a random point attractor when the Lyapunov exponent is negative, and does not converge to a point when the Lyapunov exponent is positive.
متن کاملThe moment Lyapunov exponent for conservative systems with small periodic and random perturbations
Much e ort has been devoted to the stability analysis of stationary points for linear autonomous systems of stochastic di erential equations. Here we introduce the notions of Lyapunov exponent, moment Lyapunov exponent, and stability index for linear nonautonomous systems with periodic coe cients. Most extensively we study these problems for second order conservative systems with small random a...
متن کاملLow density expansion for Lyapunov exponents
In some quasi-one-dimensional weakly disordered media, impurities are large and rare rather than small and dense. For an Anderson model with a low density of strong impurities, a perturbation theory in the impurity density is developed for the Lyapunov exponent and the density of states. The Lyapunov exponent grows linearly with the density. Anomalies of the Kappus-Wegner type appear for all ra...
متن کاملLyapunov exponents at anomalies of SL(2,R)-actions
Anomalies are known to appear in the perturbation theory for the one-dimensional Anderson model. A systematic approach to anomalies at critical points of products of random matrices is developed, classifying and analysing their possible types. The associated invariant measure is calculated formally. For an anomaly of so-called second degree, it is given by the groundstate of a certain Fokker-Pl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012