Positive Lyapunov exponent by a random perturbation

TL;DR

This paper investigates how random perturbations can induce ergodicity and positive Lyapunov exponents in certain dynamical systems that are poorly understood without perturbation, providing explicit bounds and conditions.

Contribution

It establishes conditions under which random perturbations lead to ergodic behavior and positive Lyapunov exponents in one-parameter dynamical systems, with explicit bounds.

Findings

Perturbed systems become ergodic under certain conditions.

Positive Lyapunov exponents are achieved with explicit lower bounds.

Results apply to a large set of parameter values.

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.