The K-Property of Hamiltonian Systems with Restricted Hard Ball Interactions
The K-Property of Hamiltonian Systems with Restricted Hard Ball Interactions
N. Simányi and D. Szász:
The K-Property of Hamiltonian Systems with Restricted Hard Ball Interactions
The ergodicity (K-mixing property) of the motion of $N$ elastically
colliding hard spheres in the $\nu$-dimensional ($\nu\ge 4$) flat torus
$\Bbb T^{\nu}$ is established if the hard-core interaction is the cyclic
one, i. e. the i-th ball only interacts with the $i\pm 1$-st ones.
(The indices are counted modulo $N$.) In the case $\nu=3$ we get that the
system has (countably many) {\it open} ergodic components, and the Lyapunov
exponents are almost everywhere non-zero.
The studied cyclic interaction covers the so called {\it pencase model}
of Chernov and Sinai, that is, the billiard system of $N$ hard balls in an
elongated torus, so that the balls cannot change their cyclic order in the
elongated direction.