"Hard Ball Systems Are Completely Hyperbolic."
The system of N elastically colliding hard balls
with masses M_i radius r, moving uniformly in the flat
torus is considered.
Since Sinai's celebrated 1970 paper, where he proved
hyperbolicity and even ergodicity in the case of
discs, some pleasant, `exact' properties of this particular interaction
have always been exploited in attacking the problem.
N. Simanyi, we can prove that the flow is completely
hyperbolic for almost every (N+1)-tuple
(m_1...,m_N;r) of the outer geometric parameters.
Our new, algebraic
method relies upon the very algebraic form of the equations describing the
dynamics (in analogy with geometric constructions by a compass and a ruler).