Family 150Dynamical systems and ergodic theoryNo LeanNot yet digested
Weak mixing of triangular billiards with an irrational angle
Proves that the billiard flow in every nondegenerate Euclidean triangle with at least one angle irrational relative to π is weakly mixing for normalized area times uniform direction. This strengthens ergodicity on the entire irrational-angle class, with no genericity or Diophantine restrictions.
Manuscripts in this family · 2
Weak mixing of triangular billiards with an irrational angle
Oct 5, 2026·weak-mixing-triangular-billiards.pdf
We prove that the unit-speed billiard flow in every nondegenerate Euclidean triangle with at least one angle irrational relative to π is weakly mixing for normalized Liouville measure. Equivalently, the product of the flow with itself is ergodic.
Ergodicity of triangular billiards with an irrational angle
Sep 25, 2026·Ergodicity-of-triangular-billiards-with-an-irrational-angle-September-25-2026.pdf
We prove that the unit-speed billiard flow in every nondegenerate Euclidean triangle with at least one angle irrational relative to π is ergodic for normalized area times uniform angular measure. No genericity or Diophantine condition is required. The flow is considered outside the null set of trajectories that hit a vertex.