Generating partitions for two-dimensional hyperbolic maps

For a class of two-dimensional hyperbolic maps (which includes certain billiard systems) we construct finite generating partitions. Thus, trajectories of the map can be labelled uniquely by doubly infinite symbol sequences, where the symbols correspond to the atoms of the partition. It is shown that the corresponding conditions are fulfilled in the case of the cardioid billiard, the stadium billiard (and other Bunimovich billiards), planar dispersing and semidispersing billiards.