On Omri Sarig's work on the dynamics on surfaces

We present a short survey of two major achievements of Omri Sarig’s. Both concern low-dimensional dynamics, but with very different points of view: the first one constructs Markov partitions for an general surface diffeomorphism, the second one describes invariant measures for the horocyclic flow on general infinite hyperbolic surfaces. They both are typical of Omri Sarig’s work: the sets of hypotheses are natural and possible extensions could only be reached by radically new methods.