95-374 Simanyi N., Szasz D.

The K-Property of Hamiltonian Systems with Restricted Hard Ball Interactions (71K, AMSTeX (Preprint Style)) Aug 9, 95

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Abstract. We prove the ergodicity (K-mixing property) of the hard sphere system with cyclic interactions, that is, where the i-th ball can only collide with the (i-1)-st and (i+1)-st one. (The indices are counted in a cyclic way mod N, i. e. N+1=1, 0=N.) The container of the balls is a flat torus with dimension greater than three. For three dimensions we get (countably many) open ergodic components and a. e. non-zero Lyapunov exponents. Especially we obtain the K-mixing property of the so called Chernov-Sinai pencase model (balls in an elongated torus so that these balls cannot change their cyclic order) for D=4, and open ergodic components for D=3.

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