This paper discuss a particular kind of polygonal billiards, where the sides of the billiard table can adopt only a vertical or a horizontal direction. People call those billiards VH billiards.
We generalize here a result from the 80’s by Gutkin and Katok regarding weak-mixing in VH billiards. We show that for a (Baire) generic VH billiard, the billiard dynamics is weakly mixing along a large set of directions (namely, a dense and full measure set of directions).
Alba Málaga Sabogal, Serge Troubetzkoy, (2017). “Weakly mixing polygonal billiards.” Bull. London Math. Soc.. 49 (141-147).