Weakly mixing polygonal billiards

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 \(G_δ\) dense and full measure set of directions).

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Cite :
Alba Málaga Sabogal, Serge Troubetzkoy, (2017). “Weakly mixing polygonal billiards.” Bull. London Math. Soc.. 49 (141-147).