论文标题
超扩展措施
Super-expanding measures
论文作者
论文摘要
我们研究了一维扩展的Lorenz地图，并显示了Lorens地图的致密子集的存在，因此D中的每个F中的每个F具有一组无限的不可估量的不变概率，并具有无限的Lyapunov指数和阳性熵。当奇异性自身复发时，可能会出现此类措施。相反，如果奇异性对自身的复发缓慢，则Lorenz地图具有与所有不变测度的Lyapunov指数的上限。
We study the one-dimensional expanding Lorenz maps and show the existence of dense subset D of Lorens maps such that each f in D has an uncountable set of ergodic invariant probabilities with infinite Lyapunov exponent and positive entropy. Such measures may appear when the singularity has fast recurrence to itself. Conversely, if the singularity has slow recurrence to itself then the Lorenz map has an upper bound to the Lyapunov exponent of all invariant measures.
