## Abstract

Chaotic dynamical systems are often transitive, although this transitivity is sometimes very weak.
It is of interest to divide the phase space into large regions, between which there is relatively little communication of trajectories.
We present fast, simple algorithms to find such divisions.
The present work builds on the results of [11], focussing on a statistical description of transitivity that takes into account the fact that trajectories tend to visit different regions of phase space with different frequencies.
The new work takes advantage of theoretical results from the theory of reversible Markov chains.
A new adaptive algorithm and corresponding convergence result is developed to efficiently deal with situations where the boundaries of the weakly communicating regions are complicated.