Positive Lyapunov exponent by a random perturbation

Abstract

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.

14 pages

References in corpus (1)

• From limit cycles to strange attractors

Cited by in corpus (3)

• Lyapunov exponents for random perturbations of some area-preserving maps including the standard map
• Hopf bifurcation with additive noise
• Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps