New mechanism of chaos in triangular billiards

A new mechanism of weak chaos in triangular billiards has been proposed owing to the effect of cutting of beams of rays. A similar mechanism is also implemented in other polygonal billiards. Cutting of beams results in the separation of initially close rays at a finite angle by jumps in the process of reflections of beams at the vertices of a billiard. The opposite effect of joining of beams of rays occurs in any triangular billiard along with cutting. It has been shown that the cutting of beams has an absolute character and is independent of the form of a triangular billiard or the parameters of a beam. On the contrary, joining has a relative character and depends on the commensurability of the angles of the triangle with $\pi$. Joining always suppresses cutting in triangular billiards whose angles are commensurable with $\pi$. For this reason, their dynamics cannot be chaotic. In triangular billiards whose angles are rationally incommensurable with $\pi$, cutting always dominates, leading to weak chaos. The revealed properties are confirmed by numerical experiments on the phase portraits of typical triangular billiards.