In this paper, we review several results from singularly perturbed differential equations with
multiple small parameters. In addition, we develop a general conceptual framework to …

This work presents numerical evidence that for discrete dynamical systems with one positive
Lyapunov exponent the decay of the distance autocorrelation is always related to the …

We prove the positivity of Lyapunov exponents for the normal form of a Hopf bifurcation,
perturbed by additive white noise, under sufficiently strong shear strength. This completes a …

A probabilistic approach to compute the geometric convergence rate of a stochastic process
is introduced in this paper. The goal is to quantitatively compute both the upper and lower …

In this paper we present a general result with an easily checkable condition that ensures a
transition from chaotic regime to regular regime in random dynamical systems with additive …

In this article, we review our recently introduced methods for obtaining strictly positive lower
bounds on the top Lyapunov exponent of high-dimensional, stochastic differential equations …

We study the quantitative simplicity of the Lyapunov spectrum of d-dimensional bounded
matrix cocycles subjected to additive random perturbations. In dimensions 2 and 3, we …

We study the problem of classifying stationary measures and orbit closures for non-abelian
action on a surface with a given smooth invariant measure. Using a result of Brown and …

In this paper, we give a quantitative estimate for the first N Lyapunov exponents for random
perturbations of a natural class of 2 N-dimensional volume-preserving systems exhibiting …

We study the effects of IID random perturbations of amplitude $\epsilon> 0$ on the
asymptotic dynamics of one-parameter families $\{f_a: S^ 1\to S^ 1, a\in [0, 1]\} $ of smooth …