## Hard ball systems are completely hyperbolic.(English)Zbl 0918.58040

The authors consider the system of $$N(\geq 2)$$ elastically colliding hard balls with masses $$m_1, \dots,m_N$$, radius $$r$$, moving uniformly in the flat torus $$\mathbb{T}^\nu_L= \mathbb{R}^\nu/L\cdot\mathbb{Z}^\nu$$, $$\nu\geq 2$$. 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.

### MSC:

 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 37A25 Ergodicity, mixing, rates of mixing 37A60 Dynamical aspects of statistical mechanics 37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010) 70H05 Hamilton’s equations
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