Extensions of dynamical systems and martingale approximation method

Let $T$ be a measure preserving transformation of a probability space $(\mathcal{X,F},\mu)$ and $A$ be the generator of a $\mu$-symmetric Markov process with state space $X$. Under assumption that $A$ is an “eigenvector” for $T$ an extension of $T$ is constructed in terms of $A$. By means of this extension a version of the central limit theorem is proved via approximation by martingales. Bibliography: 5 titles.