Ergodicity of billiards in every triangle with an irrational angle

Theorem 1.1 (September 25): the unit-speed billiard flow in every nondegenerate triangle with at least one angle irrational relative to $\pi$ is ergodic for normalised area times uniform angle, off the null set of vertex-hitting trajectories; consequences include quantum ergodicity and growth of nodal domain counts. The October 5 companion proves the stronger weak mixing (the product flow is ergodic). Neither proves mixing, unique ergodicity, or any statement about individual orbits (for example existence of periodic orbits in obtuse triangles), and polygons with more sides are not treated.

Theorem 1.1 (September 25): the unit-speed billiard flow in every nondegenerate triangle with at least one angle irrational relative to $\pi$ is ergodic for normalised area times uniform angle, off the null set of vertex-hitting trajectories; consequences include quantum ergodicity and growth of nodal domain counts. The October 5 companion proves the stronger weak mixing (the product flow is ergodic). Neither proves mixing, unique ergodicity, or any statement about individual orbits (for example existence of periodic orbits in obtuse triangles), and polygons with more sides are not treated.