标题： 消失的最大的李雅普诺夫指数和塔斯利斯熵 显示英文标题

标题： Vanishing largest Lyapunov exponent and Tsallis entropy

摘要： 我们提出一个几何论证，解释了为什么一些具有零最大李雅普诺夫指数的系统，其底层动力学特性可以有效地用Tsallis熵来描述。 我们依赖于Tsallis熵的广义可加性与BGS熵的普通可加性的比较。 我们通过在Tsallis熵的情况下使用配置/相空间的有效双曲度量，而在BGS熵的情况下使用欧几里得度量，将这种比较转化为度量术语。 对于这样的双曲度量求解雅可比方程，有效地将相对于相应欧几里得度量计算的最大李雅普诺夫指数设为零。 这一结论与目前所有关于具有简单渐近行为并由Tsallis熵描述的系统的已知结果一致。 显示英文摘要

摘要： We present a geometric argument that explains why some systems having vanishing largest Lyapunov exponent have underlying dynamics aspects of which can be effectively described by the Tsallis entropy. We rely on a comparison of the generalised additivity of the Tsallis entropy versus the ordinary additivity of the BGS entropy. We translate this comparison in metric terms by using an effective hyperbolic metric on the configuration/phase space for the Tsallis entropy versus the Euclidean one in the case of the BGS entropy. Solving the Jacobi equation for such hyperbolic metrics effectively sets the largest Lyapunov exponent computed with respect to the corresponding Euclidean metric to zero. This conclusion is in agreement with all currently known results about systems that have a simple asymptotic behaviour and are described by the Tsallis entropy.