Recently I become more and more interested in the field of ergodic theory, especially in the dimension theory and thermal formalism and its applications.

People always said that most of the ideas in measurable dynamics system comes from the theory of ordinary differential equation. But when I began to find the topics of ergodic theory approach into differential equation, I find there are few books directed related to it. I know there are many books discuss about the differential dynamics system (such as hyperbolic theory), however most of the books did not include the ergodic theory approach.

Are there good books and papers strongly recommend? thanks in advance.