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

Simányi, Nándor; Szász, Domokos

Ann. Math. (2) 149, No. 1, 35-96 (1999).

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.

Reviewer: Messoud Efendiev (Berlin)

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

Keywords:

elastically colliding hard balls; uniform motion; Lyapunov exponents