关于混沌动力系统Poincaré映射的分形维数

On the Fractal Dimensions of the Poincaré Maps of Chaotic Dynamical Systems

现代数值试验结果表明混沌动力系统的Poincare映射具有分形维数。然而,根据经典维数论Poincare映射根本不可能是分形的。为了解决这一现代数值试验和经典数学理论间的悖论,有必要对Poincare映射的现行定义进行修正。对此进行了若干探讨。

The results of current experiments showed that the Poincare maps of chaotic dynamical systems have fractal dimensions. However, it is rigorously proved that the Poincare maps of dynamical systems are not fractal at all according to the classical dimension theory. Such a paradox between theory and experiments can be avoided by modifying the modern definition of Poincare maps.