# Random perturbations of dynamical systems

Title: Computability and complexity of random perturbations of dynamical systems
Speaker: Cristobal Rojas

A discrete-time dynamical system is specified by a function $f$ from a space $X$ to itself.
One of the most important problems in the study of dynamical systems is to understand the limiting or
asymptotic behavior of such systems; in particular, the limiting distribution of the sequence of iterates
$$x, f(x), f(f(x)), \dots$$
Combinations of such distributions give rise to the invariant measures of the system,
which describe the asymptotic behavior in statistical terms.
In this talk we will discuss recent results on computability and complexity of such invariant measures.
In particular, we will present tight bounds on the space-complexity of computing the ergodic measure of a low-dimensional discrete-time dynamical system, affected by Gaussian random perturbations.