Nandor Simanyi


Title:  Upgrading the Theorem on Local Ergodicity

Abstract. 

We prove that in the Theorem on Local Ergodicity for Semi-Dispersive 
Billiards (proved by N. I. Chernov and Ya. G. Sinai in 1987) the condition 
of the so called ``Ansatz'' can be dropped. That condition assumed that 
almost every singular phase point had a hyperbolic trajectory after the 
singularity. Having this condition dropped, the cited theorem becomes much 
stronger and easier to apply. At the end of the talk two immediate 
corollaries of this improvement are briefly discussed: One of them is the 
(fully hyperbolic) Bernoulli mixing property of every hard disk system 
($D=2$), the other one claims that the ergodic components of every hard 
ball system ($D\ge3$) are open.