2 00 3 April 25 , 2003 Improvement of the Theorem on Local Ergodicity

We prove here that in the Theorem on Local Ergodicity for Semi-Dispersive Billiards (proved by N. I. Chernov and Ya. G. Sinai in 1987) the recently added condition on the algebraic character of the smooth boundary components of the configuration space (by P. Bálint, N. Chernov, D. Szász, and I. P. Tóth) is unnecessary. Having saved the theorem in its original form by using additional ideas in the spirit of the initial proof, the result becomes stronger and it applies to a much larger family of models. Primary subject classification: 37D50 Secondary subject classification: 34D05