Hard Ball Systems are Fully Hyperbolic

Hard Ball Systems are Fully Hyperbolic Hard Ball Systems are Fully Hyperbolic

Nándor Simányi and Domokos Szász:

Hard Ball Systems are Fully Hyperbolic

We consider the system of $N$ ($\ge 2$) elastically colliding hard balls with masses $m_1,\dots$, $m_N$, radius $r$, moving uniformly in the flat torus $\Bbb T_L^{\nu}=\Bbb R^\nu/L\cdot\Bbb Z^\nu$, $\nu\ge 2$. It is proved here that the relevant Lyapunov exponents of the flow do not vanish for almost every $(N+1)$-tuple $(m_1,\dots,m_N;L)$ of the outer geometric parameters.