硬球系统是完全双曲的
Hard ball systems are completely hyperbolic
摘要：
本文考虑N（\ge 2）个质量为m_1，.的硬球弹性碰撞系统，m_N，半径r，在平坦的环面T_L^v = R^v/L \cdot Z^v，v \ge 2.本文证明了对于几乎每一个（N+1）元组（m_1，.，m_N;L）。
英文摘要：
We consider the system of N (\ge 2) elastically colliding hard balls with masses m_1,..., m_N, radius r, moving uniformly in the flat torus T_L^ν= R^ν/L \cdot Z^ν, ν\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,...,m_N;L) of the outer geometric parameters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
